some select Q from online

What is the difference between a production function and an isoquant?

A production function describes the maximum output that can be achieved with any given combination of inputs. An isoquant identifies all of the different combinations of inputs that can be used to produce one particular level of output.

What is a production function? How does a long-run production function differ from a short-run production function?

A production function represents how inputs are transformed into outputs by a firm. In particular, a production function describes the maximum output that a firm can produce for each specified combination of inputs. In the short run, one or more factors of production cannot be changed, so a short-run production function tells us the maximum output that can be produced with different amounts of the variable inputs, holding fixed inputs constant. In the long-run production function, all inputs are variable.

The government passes a law that allows a substantial subsidy for every acre of land used to grow tobacco. How does this program affect the long-run supply curve for tobacco?

A subsidy on land used to grow tobacco decreases every farmer's average cost of producing tobacco and will lead existing tobacco growers to increase output. In addition, tobacco farmers will make positive economic profits that will encourage other firms to enter tobacco production. The result is that both the short-run and long-run supply curves for the industry will shift down and to the right.

Why does a tax create a deadweight loss? What determines the size of this loss?

A tax creates deadweight loss by artificially increasing price above the free market level, thus reducing the equilibrium quantity. This reduction in quantity reduces consumer as well as producer surplus. The size of the deadweight loss depends on the elasticities of supply and demand and on the size of the tax. The more elastic supply and demand are, the larger will be the deadweight loss. Also, the larger the tax, the greater the deadweight loss

Explain why the marginal rate of technical substitution is likely to diminish as more and more labor is substituted for capital.

As more and more labor is substituted for capital, it becomes increasingly difficult for labor to perform the jobs previously done by capital. Therefore, more units of labor will be required to replace each unit of capital, and the MRTS will diminish. For example, think of employing more and more farm labor while reducing the number of tractor hours used. At first you would stop using tractors for simpler tasks such as driving around the farm to examine and repair fences or to remove rocks and fallen tree limbs from fields. But eventually, as the number or labor hours increased and the number of tractor hours declined, you would have to plant and harvest your crops primarily by hand. This would take huge numbers of additional workers.

At the beginning of the twentieth century, there were many small American automobile manufacturers. At the end of the century, there were only three large ones. Suppose that this situation is not the result of lax federal enforcement of antimonopoly laws. How do you explain the decrease in the number of manufacturers? (Hint: What is the inherent cost structure of the automobile industry?)

Automobile plants are highly capital-intensive, and consequently there are substantial economies of scale in production. So, over time, the automobile companies that produced larger quantities of cars were able to produce at lower average cost. They then sold their cars for less and eventually drove smaller (higher cost) companies out of business, or bought them to become even larger and more efficient. At very large levels of production, the economies of scale diminish, and diseconomies of scale may even occur. This would explain why more than one manufacturer remains.

If the firm's average cost curves are U-shaped, why does its average variable cost curve achieve its minimum at a lower level of output than the average total cost curve?

Average total cost is equal to average fixed cost plus average variable cost: ATC AVC AFC. When graphed, the difference between the U-shaped average total cost and U-shaped average variable cost curves is the average fixed cost, and AFC is downward sloping at all output levels. When AVC is falling, ATC will also fall because both AVC and AFC are declining as output increases. When AVC reaches its minimum (the bottom of its U), ATC will continue to fall because AFC is falling. Even as AVC gradually begins to rise, ATC will still fall because of AFC's decline. Eventually, however, as AVC rises more rapidly, the increases in AVC will outstrip the declines in AFC, and ATC will reach its minimum and then begin to rise.

Suppose the government wants to limit imports of a certain good. Is it preferable to use an import quota or a tariff? Why?

Changes in domestic consumer and producer surpluses are the same under import quotas and tariffs. There will be a loss in (domestic) total surplus in either case. However, with a tariff, the government can collect revenue equal to the tariff times the quantity of imports, and these revenues can be redistributed in the domestic economy to offset some of the domestic deadweight loss. Thus there is less of a loss to the domestic society as a whole with a tariff. With an import quota, foreign producers can capture the difference between the domestic and world price times the quantity of imports. Therefore, with an import quota, there is a loss to the domestic society as a whole. If the national government is trying to minimize domestic welfare loss, it should use a tariff.

Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you about the nature of the production function? What does each of these shapes tell you about the MRTS?

Convex isoquants indicate that some units of one input can be substituted for a unit of the other input while maintaining output at the same level. In this case, the MRTS is diminishing as we move down along the isoquant. This tells us that it becomes more and more difficult to substitute one input for the other while keeping output unchanged. Linear isoquants imply that the slope, or the MRTS, is constant. This means that the same number of units of one input can always be exchanged for a unit of the other input holding output constant. The inputs are perfect substitutes in this case. L-shaped isoquants imply that the inputs are perfect complements, and the firm is producing under a fixed proportions type of technology. In this case the firm cannot give up one input in exchange for the other and still maintain the same level of output. For example, the firm may require exactly 4 units of capital for each unit of labor, in which case one input cannot be substituted for the other.

What is meant by deadweight loss? Why does a price ceiling usually result in a deadweight loss?

Deadweight loss refers to the benefits lost by consumers and/or producers when markets do not operate efficiently. The term deadweight denotes that these are benefits unavailable to any party. A price ceiling set below the equilibrium price in a perfectly competitive market will result in a deadweight loss because it reduces the quantity supplied by producers. Both producers and consumers lose surplus because less of the good is produced and consumed. The reduced (ceiling) price benefits consumers but hurts producers, so there is a transfer from one group to the other. The real culprit, then, and the primary source of the deadweight loss, is the reduction in the amount of the good in the market.

Is it possible to have diminishing returns to a single factor of production and constant returns to scale at the same time? Discuss.

Diminishing returns and returns to scale are completely different concepts, so it is quite possible to have both diminishing returns to, say, labor and constant returns to scale. Diminishing returns to a single factor occurs because all other inputs are fixed. Thus, as more and more of the variable factor is used, the additions to output eventually become smaller and smaller because there are no increases in the other factors. The concept of returns to scale, on the other hand, deals with the increase in output when all factors are increased by the same proportion. While each factor by itself exhibits diminishing returns, output may more than double, less than double, or exactly double when all the factors are doubled. The distinction again is that with returns to scale, all inputs are increased in the same proportion and no inputs are fixed. The production function in Exercise 10 is an example of a function with diminishing returns to each factor and constant returns to scale.

7. Because industry X is characterized by perfect competition, every firm in the industry is earning zero economic profit. If the product price falls, no firms can survive. Do you agree or disagree? Discuss.

Disagree. If the market price falls, all firms will suffer economic losses. They will cut production in the short run but continue in business as long as price is above average variable cost. In the long run, however, if price stays below average total cost, some firms will exit the industry. As firms leave industry X, the market supply decreases (i.e., shifts to the left). This causes the market price to increase. Eventually enough firms exit so that price increases to the point where profits return to zero for those firms still in the industry, and those firms will continue to survive and produce product X.

What is the difference between economic profit and producer surplus?

Economic profit is the difference between total revenue and total cost. Producer surplus is the difference between total revenue and total variable cost. So fixed cost is subtracted to find profit but not producer surplus, and thus profit equals producer surplus minus fixed cost (or producer surplus equals profit plus fixed cost).

What is the difference between economies of scale and returns to scale?

Economies of scale depend on the relationship between cost and output—i.e., how does cost change when output is doubled? Returns to scale depend on what happens to output when all inputs are doubled. The difference is that economies of scale reflect input proportions that change optimally as output is increased, while returns to scale are based on fixed input proportions (such as two units of labor for every unit of capital) as output increases.

Distinguish between economies of scale and economies of scope. Why can one be present without the other?

Economies of scale refer to the production of one good and occur when total cost increases by a smaller proportion than output. Economies of scope refer to the production of two or more goods and occur when joint production is less costly than the sum of the costs of producing each good separately. There is no direct relationship between economies of scale and economies of scope, so production can exhibit one without the other. For example, there are economies of scale producing computers and economies of scale producing carpeting, but if one company produced both, there would likely be no synergies associated with joint production and hence no economies of scope.

If a firm hires a currently unemployed worker, the opportunity cost of utilizing the worker's services is zero.

False. From the firm's point of view, the wage paid to the worker is an explicit cost whether she was previously unemployed or not. The firm's opportunity cost is equal to the wage, because if it did not hire this worker, it would have had to hire someone else at the same wage. The opportunity cost from the worker's point of view is the value of her time, which is unlikely to be zero. By taking this job, she cannot work at another job or take care of a child or elderly person at home. If her best alternative is working at another job, she gives up the wage she would have earned. If her best alternative is unpaid, such as taking care of a loved one, she will now have to pay someone else to do that job, and the amount she has to pay is her opportunity cost.

9. True or false: A firm should always produce at an output at which long-run average cost is minimized. Explain.

False. In the long run, under perfect competition, firms will produce where long-run average cost is minimized. In the short run, however, it may be optimal to produce at a different level. For example, if price is above the long-run equilibrium price, the firm will maximize short-run profit by producing a greater amount of output than the level at which LAC is minimized as illustrated in the diagram. PL is the long-run equilibrium price, and qL is the output level that minimizes LAC. If price increases to P in the short run, the firm maximizes profit by producing q′, which is greater than qL, because that is the output level at which SMC (short-run marginal cost) equals price

Why do firms enter an industry when they know that in the long run economic profit will be zero?

Firms enter an industry when they expect to earn economic profit, even if the profit will be short-lived. These short-run economic profits are enough to encourage entry because there is no cost to entering the industry, and some economic profit is better than none. Zero economic profit in the long run implies normal returns to the factors of production, including the labor and capital of the owner of the firm. So even when economic profit falls to zero, the firm will be doing as well as it could in any other industry, and then the owner will be indifferent to staying in the industry or exiting.

A firm has a production process in which the inputs to production are perfectly substitutable in the long run. Can you tell whether the marginal rate of technical substitution is high or low, or is further information necessary? Discuss.

Further information is necessary. The marginal rate of technical substitution, MRTS, is the absolute value of the slope of an isoquant. If the inputs are perfect substitutes, the isoquants will be linear. To calculate the slope of the isoquant, and hence the MRTS, we need to know the rate at which one input may be substituted for the other. In this case, we do not know whether the MRTS is high or low. All we know is that it is a constant number. We need to know the marginal product of each input to determine the MRTS.

Suppose a competitive industry faces an increase in demand (i.e., the demand curve shifts upward). What are the steps by which a competitive market insures increased output? Will your answer change if the government imposes a price ceiling?

If demand increases, price and profits increase in the short run. The price increase causes existing firms to increase output, and the positive profits induce new firms to enter the industry in the long run, shifting the supply curve to the right. This results in a new equilibrium with a higher quantity and a price (less than the short-run price) that earns all firms zero economic profit. With an effective price ceiling, price will not increase when demand increases, and firms will therefore not increase output. Also, without an increase in economic profit, no new firms enter, and there is no shift in the supply curve. So the result is very different with a price ceiling. Output does not increase as a result of the increase in demand. Instead there is a shortage of the product.

A chair manufacturer hires its assembly-line labor for $30 an hour and calculates that the rental cost of its machinery is $15 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 3 hours of labor for each hour of machine time, is it minimizing its costs of production? If so, why? If not, how can it improve the situation? Graphically illustrate the isoquant and the two isocost lines for the current combination of labor and capital and for the optimal combination of labor and capital.

If the firm can produce one chair with either four hours of labor or four hours of machinery (i.e., capital), or any combination, then the isoquant is a straight line with a slope of −1 and intercepts at K 4 and L 4, as depicted by the dashed line. The isocost lines, TC 30L 15K, have slopes of 30/15 2 when plotted with capital on the vertical axis and intercepts at K TC/15 and L TC/30. The cost minimizing point is the corner solution where L 0 and K 4, so the firm is not currently minimizing its costs. At the optimal point, total cost is $60. Two isocost lines are illustrated on the graph. The first one is further from the origin and represents the current higher cost ($105) of using 3 labor and 1 capital. The firm will find it optimal to move to the second isocost line which is closer to the origin, and which represents a lower cost ($60). In general, the firm wants to be on the lowest isocost line possible, which is the lowest isocost line that still intersects or touches the given isoquant.

How can a price ceiling make consumers better off? Under what conditions might it make them worse off?

If the supply curve is highly inelastic a price ceiling will usually increase consumer surplus because the quantity available will not decline much, but consumers get to purchase the product at a reduced price. If the demand curve is inelastic, on the other hand, price controls may result in a net loss of consumer surplus because consumers who value the good highly are unable to purchase as much as they would like. The loss of consumer surplus is greater than the transfer of producer surplus to consumers. So consumers are made better off when demand is relatively elastic and supply is relatively inelastic, and they are made worse off when the opposite is true

You are an employer seeking to fill a vacant position on an assembly line. Are you more concerned with the average product of labor or the marginal product of labor for the last person hired? If you observe that your average product is just beginning to decline, should you hire any more workers? What does this situation imply about the marginal product of your last worker hired?

In filling a vacant position, you should be concerned with the marginal product of the last worker hired, because the marginal product measures the effect on output, or total product, of hiring another worker. This in turn determines the additional revenue generated by hiring another worker, which should then be compared to the cost of hiring the additional worker. The point at which the average product begins to decline is the point where average product is equal to marginal product. As more workers are used beyond this point, both average product and marginal product decline. However, marginal product is still positive, so total product continues to increase. Thus, it may still be profitable to hire another worker.

Explain why the industry supply curve is not the long-run industry marginal cost curve.

In the short run, a change in the market price induces the profit-maximizing firm to change its optimal level of output. This optimal output occurs where price is equal to marginal cost, as long as marginal cost exceeds average variable cost. Therefore, the short-run supply curve of the firm is its marginal cost curve, above average variable cost. (When the price falls below average variable cost, the firm will shut down.) In the long run, a change in the market price induces entry into or exit from the industry and may induce existing firms to change their optimal outputs as well. As a result, the prices firms pay for inputs can change, and these will cause the firms' marginal costs to shift up or down. Therefore, long-run supply is not the sum of the existing firms' long-run marginal cost curves. The long-run supply curve depends on the number of firms in the market and on how their costs change due to any changes in input costs. As a simple example, consider a constant-cost industry where each firm has a U-shaped LAC curve. Here the input prices do not change, only the number of firms changes when industry price changes. Each firm has an increasing LMC, but the industry long-run supply is horizontal because any change in industry output comes about by firms entering or leaving the industry, not by existing firms moving up or down their LMC curves.

Suppose that output q is a function of a single input, labor (L). Describe the returns to scale associated with each of the following production functions: q L/2.

Let q be output when labor is doubled to 2L. Then q (2L)/2 L. Compare q to q by dividing q by q. This gives us q/q L/(L/2) 2. Therefore when the amount of labor is doubled, output is also doubled. Hence there are constant returns to scale.

Why would a firm that incurs losses choose to produce rather than shut down?

Losses occur when revenues do not cover total costs. If revenues are greater than variable costs, but not total costs, the firm is better off producing in the short run rather than shutting down, even though it is incurring a loss. The reason is that the firm will be stuck will all its fixed cost and have no revenue if it shuts down, so its loss will equal its fixed cost. If it continues to produce, however, and revenue is greater than variable costs, the firm can pay for some of its fixed cost, so its loss is less than it would be if it shut down. In the long run, all costs are variable, and thus all costs must be covered if the firm is to remain in business.

Explain the term "marginal rate of technical substitution." What does a MRTS 4 mean?

MRTS is the amount by which the quantity of one input can be reduced when the other input is increased by one unit, while maintaining the same level of output. If the MRTS is 4 then one input can be reduced by 4 units as the other is increased by one unit, and output will remain the same.

Can a firm have a production function that exhibits increasing returns to scale, constant returns to scale, and decreasing returns to scale as output increases? Discuss.

Many firms have production functions that exhibit first increasing, then constant, and ultimately decreasing returns to scale. At low levels of output, a proportional increase in all inputs may lead to a larger-than-proportional increase in output, because there are many ways to take advantage of greater specialization as the scale of operation increases. As the firm grows, the opportunities for specialization may diminish, and the firm operates at peak efficiency. If the firm wants to double its output, it must duplicate what it is already doing. So it must double all inputs in order to double its output, and thus there are constant returns to scale. At some level of production, the firm will be so large that when inputs are doubled, output will less than double, a situation that can arise from management diseconomies.

Can an isoquant ever slope upward? Explain.

No. An upward sloping isoquant would mean that if you increased both inputs output would stay the same. This would occur only if one of the inputs reduced output; sort of like a bad in consumer theory. As a general rule, if the firm has more of all inputs it can produce more output.

Is the firm's expansion path always a straight line?

No. If the firm always uses capital and labor in the same proportion, the long run expansion path is a straight line. But if the optimal capital-labor ratio changes as output is increased, the expansion path is not a straight line.

Assume that the marginal cost of production is increasing. Can you determine whether the average variable cost is increasing or decreasing? Explain.

No. When marginal cost is increasing, average variable cost can be either increasing or decreasing as shown in the diagram below. Marginal cost begins increasing at output level q1, but AVC is decreasing. This happens because MC is below AVC and is therefore pulling AVC down. AVC is decreasing for all output levels between q1 and q2. At q2, MC cuts through the minimum point of AVC, and AVC begins to rise because MC is above it. Thus for output levels greater than q2, AVC is increasing.

Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of production is given by C 200 2q2, where q is the level of output and C is total cost. (The marginal cost of production is 4q; the fixed cost is $200.) a. If the price of watches is $100, how many watches should you produce to maximize b.What will the profit level be? At what minimum price will the firm produce a positive output?

Profits are maximized where price equals marginal cost. Therefore, 100 = 4q, or q = 25. Profit is equal to total revenue minus total cost: pi = pq - (200+2q^2) pi = (100)(25) -(200+2(25)^2)=1050 So, MC is greater than AVC for any quantity greater than 0. This means that the firm produces in the short run as long as price is positive.

Joe quits his computer programming job, where he was earning a salary of $50,000 per year, to start his own computer software business in a building that he owns and was previously renting out for $24,000 per year. In his first year of business he has the following expenses: salary paid to himself, $40,000; rent, $0; other expenses, $25,000. Find the accounting cost and the economic cost associated with Joe's computer software business.

The accounting cost includes only the explicit expenses, which are Joe's salary and his other expenses: $40,000 25,000 $65,000. Economic cost includes these explicit expenses plus opportunity costs. Therefore, economic cost includes the $24,000 Joe gave up by not renting the building and an extra $10,000 because he paid himself a salary $10,000 below market ($50,000 40,000). Economic cost is then $40,000 25,000 24,000 10,000 $99,000.

The cost of flying a passenger plane from point A to point B is $50,000. The airline flies this route four times per day at 7 AM, 10 AM, 1 PM, and 4 PM. The first and last flights are filled to capacity with 240 people. The second and third flights are only half full. Find the average cost per passenger for each flight. Suppose the airline hires you as a marketing consultant and wants to know which type of customer it should try to attract—the off-peak customer (the middle two flights) or the rush-hour customer (the first and last flights). What advice would you offer?

The average cost per passenger is $50,000/240 = $208.33 for the full flights and $50,000/120 = $416.67 for the half full flights. The airline should focus on attracting more off-peak customers because there is excess capacity on the middle two flights. The marginal cost of taking another passenger on those two flights is almost zero, so the company will increase its profit if it can sell additional tickets for those flights, even if the ticket prices are less than average cost. The peak flights are already full, so attracting more customers at those times will not result in additional ticket sales.

The owner of a small retail store does her own accounting work. How would you measure the opportunity cost of her work?

The economic, or opportunity, cost of doing accounting work is measured by computing the monetary amount that the owner's time would be worth in its next best use. For example, if she could do accounting work for some other company instead of her own, her opportunity cost is the amount she could have earned in that alternative employment. Or if she is a great stand-up comic, her opportunity cost is what she could have earned in that occupation instead of doing her own accounting work.

How does a change in the price of one input change the firm's long-run expansion path?

The expansion path describes the cost-minimizing combination of inputs that the firm chooses for every output level. This combination depends on the ratio of input prices, so if the price of one input changes, the price ratio also changes. For example, if the price of an input increases, the intercept of the isocost line on that input's axis moves closer to the origin, and the slope of the isocost line (the price ratio) changes. As the price ratio changes, the firm substitutes away from the now more expensive input toward the cheaper input. Thus the expansion path bends toward the axis of the now cheaper input.

Why are isocost lines straight lines?

The isocost line represents all possible combinations of two inputs that may be purchased for a given total cost. The slope of the isocost line is the negative of the ratio of the input prices. If the input prices are fixed, their ratio is constant and the isocost line is therefore straight. Only if the ratio of the input prices changes as the quantities of the inputs change is the isocost line not straight.

An increase in the demand for movies also increases the salaries of actors and actresses. Is the long-run supply curve for films likely to be horizontal or upward sloping? Explain.

The long-run supply curve depends on the cost structure of the industry. Assuming there is a relatively fixed supply of actors and actresses, as more films are produced, higher salaries must be offered. Therefore the industry experiences increasing costs. In an increasing-cost industry, the long-run supply curve is upward sloping. Thus the supply curve for films would be upward sloping.

The menu at Joe's coffee shop consists of a variety of coffee drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers who can be served by that worker in a given time period. Joe has been employing one worker, but is considering hiring a second and a third. Explain why the marginal product of the second and third workers might be higher than the first. Why might you expect the marginal product of additional workers to diminish eventually?

The marginal product could well increase for the second and third workers because each would be able to specialize in a different task. If there is only one worker, that person has to take orders, prepare the food, serve the food, and do all the cleanup. With two or three workers, however, one could take orders and serve the food while the others do most of the coffee and food preparation and cleanup. Eventually, however, as more workers are employed, the marginal product would diminish because there would be a large number of people behind the counter and in the kitchen trying to serve more and more customers with a limited amount of equipment and a fixed building size.

Why is the marginal product of labor likely to increase initially in the short run as more of the variable input is hired?

The marginal product of labor is likely to increase initially because when there are more workers, each is able to specialize in an aspect of the production process in which he or she is particularly skilled. For example, think of the typical fast food restaurant. If there is only one worker, he will need to prepare the burgers, fries, and sodas, as well as take the orders. Only so many customers can be served in an hour. With two or three workers, each is able to specialize, and the marginal product (number of customers served per hour) is likely to increase as we move from one to two to three workers. Eventually, there will be enough workers and there will be no more gains from specialization. At this point, the marginal product will begin to diminish.

Suppose that labor is the only variable input to the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labor?

The marginal product of labor must be increasing. The marginal cost of production measures the extra cost of producing one more unit of output. If this cost is diminishing, then it must be taking fewer units of labor to produce the extra unit of output. If fewer units of labor are required to produce a unit of output, then the marginal product (extra output produced by an extra unit of labor) must be increasing. Note also, that MC w/MPL, so that if MC is diminishing then MPL must be increasing for any given w.

Why does production eventually experience diminishing marginal returns to labor in the short run?

The marginal product of labor will eventually diminish because there will be at least one fixed factor of production, such as capital. As more and more labor is used along with a fixed amount of capital, there is less and less capital for each worker to use, and the productivity of additional workers necessarily declines. Think for example of an office where there are only three computers. As more and more employees try to share the computers, the marginal product of each additional employee will diminish.

The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of capital?

The marginal rate of technical substitution is defined at the ratio of the two marginal products. Here, we are given the marginal product of labor and the marginal rate of technical substitution. To determine the marginal product of capital, substitute the given values for the marginal product of labor and the marginal rate of technical substitution in the following formula: (MPL/MPK) = -MRTS, or, 50/MPK = 1/4 and therefore, MPK 200 computer chips per hour.

A political campaign manager must decide whether to emphasize television advertisements or letters to potential voters in a reelection campaign. Describe the production function for campaign votes. How might information about this function (such as the shape of the isoquants) help the campaign manager to plan strategy?

The output of concern to the campaign manager is the number of votes. The production function has two inputs, television advertising and letters. The use of these inputs requires knowledge of the substitution possibilities between them. If the inputs are perfect substitutes for example, the isoquants are straight lines, and the campaign manager should use only the less expensive input in this case. If the inputs are not perfect substitutes, the isoquants will have a convex shape. The campaign manager should then spend the campaign's budget on the combination of the two inputs that maximize the number of votes.

Suppose a chair manufacturer finds that the marginal rate of technical substitution of capital for labor in her production process is substantially greater than the ratio of the rental rate on machinery to the wage rate for assembly-line labor. How should she alter her use of capital and labor to minimize the cost of production?

The question states that the MRTS of capital for labor is greater than r/w. Note that this is different from the MRTS of labor for capital, which is what is used in Chapters 6 and 7. The MRTS of labor for capital equals MPK/MPL. So it follows that MPK/MPL > r/w or, written another way, MPK/r > MPL/w. These two ratios should be equal to minimize cost. Since the manufacturer gets more marginal output per dollar from capital than from labor, she should use more capital and less labor to minimize the cost of production.

What assumptions are necessary for a market to be perfectly competitive? In light of what you have learned in this chapter, why is each of these assumptions important?

The three primary assumptions of perfect competition are (1) all firms in the industry are price takers, (2) all firms produce identical products, and (3) there is free entry and exit of firms to and from the market. The first two assumptions are important because they imply that no firm has any market power and that each faces a horizontal demand curve. As a result, firms produce where price equals marginal cost, which defines their supply curves. With free entry and exit, positive (negative) economic profits encourage firms to enter (exit) the industry. Entry and exit affect industry supply and price. In the long run, entry or exit continues until price equals long-run average cost and firms earn zero economic profit.

A firm pays its accountant an annual retainer of $10,000. Is this an economic cost?

This is an explicit cost of purchasing the services of the accountant, and it is both an economic and an accounting cost. When the firm pays an annual retainer of $10,000, there is a monetary transaction. The accountant trades his or her time in return for money. An annual retainer is an explicit cost and therefore an economic cost.

Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. a. How does this tax affect the firm's fixed, marginal, and average costs? b. Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how does this tax affect the firm's fixed, marginal, and average costs?

This tax is a fixed cost because it does not vary with the quantity of output produced. If T is the amount of the tax and F is the firm's original fixed cost, the new total fixed cost increases to TFC T F. The tax does not affect marginal or variable cost because it does not vary with output. The tax increases both average fixed cost and average total cost by T/q. Let t equal the per unit tax. When a tax is imposed on each unit produced, total variable cost increases by tq and fixed cost does not change. Average variable cost increases by t, and because fixed costs are constant, average total cost also increases by t. Further, because total cost increases by t for each additional unit produced, marginal cost increases by t.

A firm that has positive accounting profit does not necessarily have positive economic profit.

True. Accounting profit considers only the explicit, monetary costs. Since there may be some opportunity costs that were not fully realized as explicit monetary costs, it is possible that when the opportunity costs are added in, economic profit will become negative. This indicates that the firm's resources are not being put to their best use.

If the owner of a business pays himself no salary, then the accounting cost is zero, but the economic cost is positive.

True. Since there is no monetary transaction, there is no accounting, or explicit, cost. However, since the owner of the business could be employed elsewhere, there is an economic cost. The economic cost is positive, reflecting the opportunity cost of the owner's time. The economic cost is the value of the owner's time in his next best alternative, or the amount that the owner would earn if he took the next best job.

9. The short-run cost function of a company is given by the equation TC 200 55q, where TC is the total cost and q is the total quantity of output, both measured in thousands. a. What is the company's fixed cost? b. If the company produced 100,000 units of goods, what would be its average variable cost? What would be its average fixed cost?

When q = 0, TC = 200, so fixed cost is equal to 200 (or $200,000). With 100,000 units, q = (55)(100) = 5500 (or $5,500,000). Average variable cost is VC/q = 5500/100 = 55 At q = 100, average fixed cost is 200/100= 2 (or $2000).

If a firm enjoys economies of scale up to a certain output level, and cost then increases proportionately with output, what can you say about the shape of the long-run average cost curve?

When the firm experiences economies of scale, its long-run average cost curve is downward sloping. When costs increase proportionately with output, the firm's long-run average cost curve is horizontal. So this firm's long-run average cost curve has a rounded L-shape; first it falls and then it becomes horizontal as output increases.

Suppose the supply curve for a good is completely inelastic. If the government imposed a price ceiling below the market-clearing level, would a deadweight loss result? Explain.

When the supply curve is completely inelastic, it is vertical. In this case there is no deadweight loss because there is no reduction in the amount of the good produced. The imposition of the price ceiling transfers all lost producer surplus to consumers. Consumer surplus increases by the difference between the market-clearing price and the price ceiling times the market-clearing quantity. Consumers capture all decreases in total revenue, and no deadweight loss occurs.

Faced with constantly changing conditions, why would a firm ever keep any factors fixed? What criteria determine whether a factor is fixed or variable?

Whether a factor is fixed or variable depends on the time horizon under consideration: all factors are fixed in the very short run while all factors are variable in the long run. As stated in the text, "All fixed inputs in the short run represent outcomes of previous long-run decisions based on estimates of what a firm could profitably produce and sell." Some factors are fixed in the short run, whether the firm likes it or not, simply because it takes time to adjust the levels of those inputs. For example, a lease on a building may legally bind the firm, some employees may have contracts that must be upheld, or construction of a new facility may take a year or more. Recall that the short run is not defined as a specific number of months or years but as that period of time during which some inputs cannot be changed for reasons such as those given above.

. Suppose the government regulates the price of a good to be no lower than some minimum level. Can such a minimum price make producers as a whole worse off? Explain.

With a minimum price set above the market-clearing price, some consumer surplus is transferred to producers because of the higher price, but some producer surplus is lost because consumers purchase less. If demand is highly elastic, the reduction in purchases can offset the higher price producers receive, making producers worse off. In the diagram below, the market-clearing price and quantity are P0 and Q0. The minimum price is set at P, and at this price consumers demand Q. Assuming that suppliers produce Q (and not the larger quantity indicated by the supply curve), producer surplus increases by area A due to the higher price, but decreases by the much larger area B because the quantity demanded drops sharply. The result is a reduction in producer surplus.

A certain brand of vacuum cleaners can be purchased from several local stores as well as from several catalogues or websites. a. If all sellers charge the same price for the vacuum cleaner, will they all earn zero economic profit in the long run? If all sellers charge the same price and one local seller owns the building in which he does business, paying no rent, is this seller earning a positive economic profit?

Yes, all earn zero economic profit in the long run. If economic profit were greater than zero for, say, online sellers, then firms would enter the online industry and eventually drive economic profit for online sellers to zero. If economic profit were negative for catalogue sellers, some catalogue firms would exit the industry until economic profit returned to zero. So all must earn zero economic profit in the long run. Anything else will generate entry or exit until economic profit returns to zero. No this seller would still earn zero economic profit. If he pays no rent then the accounting cost of using the building is zero, but there is still an opportunity cost, which represents the value of the building in its best alternative use.

Assume that the marginal cost of production is greater than the average variable cost. Can you determine whether the average variable cost is increasing or decreasing? Explain.

Yes, the average variable cost is increasing. If marginal cost is above average variable cost, each additional unit costs more to produce than the average of the previous units, so the average variable cost is pulled upward. This is shown in the diagram above for output levels greater than q2.

Can there be constant returns to scale in an industry with an upward-sloping supply curve? Explain.

Yes. Constant returns to scale means that proportional increases in all inputs yield the same proportional increase in output. However, when all firms increase their input use, the prices of some inputs may rise, because their supply curves are upward sloping. For example, production that uses rare or depleting inputs will see higher input costs as production increases. Doubling inputs will still yield double output, but because of rising input prices, production costs will more than double. In this case the industry is an increasing-cost industry, and it will have an upward-sloping long-run supply curve. Therefore, an industry can have both constant returns to scale and an upward-sloping industry supply curve.

In long-run equilibrium, all firms in the industry earn zero economic profit. Why is this true?

participants in an industry. With free entry, positive economic profits induce new entrants. As these firms enter, the supply curve shifts to the right, causing a fall in the equilibrium price of the product. Entry will stop, and equilibrium will be achieved, when economic profits have fallen to zero. Some firms may earn greater accounting profits than others because, for example, they own a superior source of an important input, but their economic profits will be the same. To be more concrete, suppose one firm can mine a critical input for $2 per pound while all other firms in the industry have to pay $3 per pound. The one firm will have an accounting cost advantage and will report higher accounting profits than other firms in the industry. But there is an opportunity cost associated with the company's input use, because other firms would be willing to pay up to $3 per pound to buy the input from the firm with the superior mine. Therefore, the company should include a $1 per pound opportunity cost for using its own input rather than selling it to other firms. Then, that firm's economic costs and economic profit will be the same as all the other firms in the industry. So all firms will earn zero economic profit in the long run.