Managerial Economics - Costs of Production and Org of the Firm
A private college adds a small café to its building to cater to the needs of its own students. The total cost of the facilities for the café is $100,000. After a year of operations the college determines that operating the café is interfering with its primary business of educating students. A group of enterprising business students offer to purchase the café facilities for $50,000. The college balks at the idea because it had paid $100,000 for the facilities. The college spends $10,000 advertising the café for sale hoping to get an outside buyer willing to pay much more than the students and operate the café on campus. When no outside offer was forthcoming the students increased their offer to $55,000. Should the college take the students' offer? Why or why not?
$110,000 (cost of the facility plus the advertising cost) are sunk costs meaning that they cannot be recovered. Since the cost cannot be recovered, the college should take the students second offer since it's the best offer.
Methods of procuring inputs
- Purchase the inputs using spot exchange - Acquire inputs under a contract - Produce the inputs internally
Contract
A formal relationship between a buyer and a seller that obligates the buyer and seller to exchange at terms specified in a legal document.
Multiple Cost functions
A function that defines the cost of producing given levels of two or more types of outputs assuming all inputs are used efficiently.
The Production Function
A function that defines the maximum amount of output that can be produced with a given set of inputs. Mathematically, the production function is denoted as Q = F(K,L) where K is the units of capital and L units of labour.
Short run cost function
A function that defines the minimum possible cost of producing each output level when variable factors are employed in the cost minimizing fashion.
Isocosts
A line that represents the combinations of inputs that will cost the producer the same amount of money
Law of diminishing marginal rate of technical subsitution
A property of a production function stating that as less of one input is used, increasing amounts of another input must be employed to produce the same level of output.
Vertical Integration
A situation where a firm produces the inputs required to make its final product.
Law of diminishing marginal returns
As more of a variable resource is added to a given amount of a fixed resource, marginal product eventually declines and could become negative
Principle: Phases of Marginal Returns
As the usage of an input increases, marginal product initially increases (increasing marginal returns), then begins to decline (decreasing marginal returns), and eventually becomes negative (negative marginal returns).
Isoquants
Convex curves showing all possible combinations of inputs that yield the same output
Assume that a firm hires only labour and capital to produce bicycles. Explain the cost minimization rule for this firm and why this rule is logical?
Cost minimization rule is a basic rule which is used by the producers to determine what mix of labour and capital produces output at lowest cost or what is the most effective cost method that can be used for producing goods and services to maximize profits. The rule is logical because total cost is minimized at level of capital and labour in such a way that the marginal product of labour is divided by the wage is equal to the marginal product of capital divided by the rental price of the capital. Marginal products per dollar are equal. Where wage is (w) and capital is (r). Here in this case the firm needs only labour and capital to produce bicycles so, cost can be looked as being minimized and production being most effective when the additional output per capital spent on producing each bicycle is the same from Labour. Formula for cost minimization rule is MPL/w= MPK/r.
Long-Run production
Defined as the horizon over which the manager can adjust all factors of production
Irrelevance of sunk costs
Sunk costs are costs that are forever lost after it h as been paid so a decision maker should ignore these types of costs to max profits or min losses.
The three most important measures of productivity
TP - maximum level of output that can be produced with a given amount of time AP - a measure of the output produced per unit of input ex: (AP labour = Q/L) MP- the change in total output attributable to the last unit of an input ex: MP capital = change in Q/ change in K
Provide a typical graph of TVC and explain how it is related to the TP curve. Provide a single graph showing the typical behaviour of AVC and MC. Be sure to label your axes correctly. Explain how the AVC and MC curves are related to the AP and MP curves.
TVC is explained by TP and they have an opposing relationship. That is, when TP increases at an increasing rate then TVC will increase at a decreasing rate. On the the other hand, when TVC increases at an increasing rate then conversely TP will increase at a decreasing rate. Both MC and AVC have U-shaped curves that fall and increase but MC will rise faster than AVC. The two will intersect where AVC is at a minimum. · When MC<AVC, AVC falls. · When MC>AVC, AVC rises. MC is determined by the level of MP. · As MP rises, MC falls · As MP falls, MC increases AVC is explained by AP. · When AP increase, AVC falls When AP falls, AVC increases
Marginal (incremental) cost
The change is total costs arising from a change in the managerial control variable Q MC = change in C/ change in Q
Marginal rate of technical substitution
The rate at which a producer can substitute between two inputs and maintain the same level of output. MRTS (k,l) = MP labour * MP capital
Provide a typical graph of the total product and explain why it has that shape. Provide a single graph showing the typical behaviour of average product and marginal product. Be sure to label your axes correctly. Explain how MP is related to TP and to AP.
The shape of TP reflects the behaviour of MP. In the short-run, because of fixed capital, MP increases then falls. As MP increases TP increases at an increasing rate as its slope increases. Diminishing MP cause TP to increase at a decreasing rate as its slope falls. See Figure 5-1 on page 139 for a typical graph. AP = TP /Q and MP = change Q/ change L, are per unit concepts and, therefore, much smaller that total output. MP and AP rise then fall because of the law of diminishing marginal and average returns, respectively. MP is the slope of TP. MP increases faster and falls faster than AP. MP intersects AP at the maximum AP. If MP>AP, AP rises. If MP<AP, AP falls. \
Value marginal product
The value of the output produced by the last unit of an input For example: If each unit of output can be sold at price P, the value marginal product of labour is VMPL = P * MPL
Short-Run Production
Time frame in which there are fixed factors of production. Short run is essentially only a function of labour since capital is fixed rather than variable.
Principle: Profit-Maximizing Input Usage
To maximize profits, a manager should use inputs at levels at which the marginal benefit equals the marginal cost. More specifically, when the cost of each additional unit of labour is w, the manger should continue to employ labour up to the point where VMPL = w in the range of diminishing marginal product.
Principle: Optimal Input substitution
To minimize the cost of producing a given level of output, the firm should use less of an input and more of other inputs when that input's price rises.
Principle: Cost-mInimizing input rule
To minimize the cost of producing a given level of output, the marginal product per dollar spent should be equal for all inputs: MP labour / w = MP capital / r Equivalently, to min the cost of production, a firm should employ inputs such that the marginal rate of technical substitution is equal to the ratio of input prices: MP labour/ MP capital = w/r
Cost Complementarity
When the marginal cost of producing one type of output decreases when the output of another good is increased. Example: Doughnuts and doughnut hole production.
Principal Agent Problem
a problem caused by an agent pursuing his own interests rather than the interests of the principal who hired him
Consider the following production function: Q= K ^ 2/3 L^⅓ . Explain the special characteristics of this production function. How is it different from a Linear production function? How is it different from a Leontief production function?
· K^(2/3)L^1/3 is a Cobb Douglas Production Function · This Production Function exhibit Constant Return to scale as: Q(tK,tL)= t K^(2/3)*L^(1/3) = tQ(K,L) · Elasticity of substitution for this production function is 1 i.e., (percentage change in K/L)/(percentage change in MRTS) = 1 · As the equation suggests, it is a convex function · MRTS is diminishing · Linear function is a perfect substitute of inputs case · MRTS of given function is diminishing while MRTS of linear is constant · Elasticity of substitution of function given is 1 while elasticity of substitution for linear production function is infinity · Leontieff production function is an L shaped curve · Elasticity of substitution of function given is 1 while elasticity of substitution for Leontieff production function is zero
Explain the differences between economies of scale, economies of scope and cost complementarity. Provide one example of each.
Economies of scale exist whenever long-run average costs decline as output increases. This occurs when firms expand their plant sizes in order to take advantage of better technology, more specialized labour, etc. to lower ATC. For many technologies, there is a range over which economies of scale exist and a range over which diseconomies exist. Economies of scope exist when the joint production of two goods is less expensive that the production of both goods separately. Economies of scope are an important reason why firms produce multiple products. For example, it may be more efficient to produce both cars and light trucks in a single plant than to produce both good separately, the two products may share many parts of the same assembly (such as the chassis) and producing the products separately would require considerable duplicative construction. Samsung produces various smartphone brands in the same factory. Cost complementarities exist when the marginal cost of producing one output is reduced when the output of another product is increase. That is, when an increase in the output of product 2 decreases the marginal cost of producing output 1. A simple example is doughnuts and doughnut holes. Multiproduct firms that enjoy cost complementarities tend to have lower marginal costs than firms producing a single product.
Economies of Scope
Exist when the total cost of producing two products within the same firm is lower than when the products are produced by separate firms. Example: It is most likely cheaper for a restaurant to make chicken and steak dinners rather than having two separate restaurants specialize in one or the other. The reason for this is that making the dinner would require duplication of many common factors of production such as ovens, fridges, etc.
Principle: Changes in Isocosts
For given input prices, isocosts farther from the origin are associated with higher costs. Changes in input prices change the slopes of isocost lines.
Explain how the firm would use the marginal product of labour to determine the profit maximizing quantity of labour which the firm would hire.
For profit maximization we have to maximize the following as profit = TR -TC Firms use the above equations to determine profit maximizing by evaluating quantity of labour and capital. To determine L and K, such that MPL =w/P and MPK = v/P. Firms should continue to hire labour until VMPL = W. In perfect competition, firms should continue to hire labour until VMPL = MPL*P where p = price of the product.
Assuming that the cost of capital is $1,000 and labour costs $10.00 per hour, determine the total variable cost, average variable cost, and the marginal cost of the firm for the output levels given above.
Here, L is the only variable factor, TVC is the product of 10 and L (TVC=10*L). AVC is the ratio of TVC to Q, the quantity of output produced. The MC is the additional cost by producing additional output.
Assume that a firm hires only labour and capital to produce bicycles. If the price of capital falls to $4.00 what should the firm do to minimize cost? Explain why your answer is consistent with the cost minimization rule.
If the price falls to $4, this is when MPL/w is not equal to MPK/r this is when the inputs are not in balance thus MPL/w > MPK/r. To reduce cost in this situation where marginal product of labour divided by the wage is greater than that of marginal product of capital divided by the rental price of the capital. According to the concept of diminishing marginal product, It is. firm must hire more capital and less labour to reduce MPK and increase MPL until MPK/w is equal to MPL/w.
Explain why the short run ATC is U-shaped? Explain why the long-run ATC is also U-shaped? How are the two curves different?
In the long-run, all costs are variable because the manager is free to adjust the levels of all inputs. The long-run AVC is the lower envelope of all the short-run of all short-run AVC. What does this mean? The curve is U-shaped in this case because of economies and diseconomies of scale. This implies that initially an expansion of output allows the firm to produce at a lower long-run average cost. This is because the plant size is increased. When there are economies of scale, increasing the size of operation decreases the minimum average cost. A larger plant lowers ATC because of its use of mass production techniques, better technology, quality labour, etc. However, after a point, further increases in output will lead to an increase in average costs and this is known as diseconomies of scale. In real-life, this is shown as a facility and operations get larger then eventually management and labour will not be able to keep up.
Managerial Compensation
Incentives can be used to align management and stockholder interests The incentives need to be structured carefully to make sure that they achieve their goal
Long-run costs and economies of scale
Long run average cost curves are U shaped which implies that initially an expansion, of output allows the firm to produce at lower long-run average cost as is shown for outputs between 9 and Q*. This condition is known as economies of scale. When there are economies of scale, increasing the size of the operation decreases the min av cost. After a point, such as Q*, further increases in output lead to an increase in average costs. This condition is known as diseconomies of scale. Sometimes the technology in an industry allows a firm to produce different levels of output at the same min average cost, this is called constant returns to scale.
Assume that a firm hires only labour and capital to produce bicycles. Suppose that the firm hires 100 units of capital and 500 units of labour and that the MPl is 20 while MPk is 25. If a unit of labour costs $4.00 and a unit of capital costs $5.00, is the firm minimizing costs? Explain
MPL/w = MPk/r so 20/4 = 25/5 =$5 per unit Yes, the firm is minimizing cost at the level of capital and labour in such a way that marginal product of labour divided by the wage is equal to that of marginal product of the capital divided by the rental price of capital, so here clearly the cost has been effectively minimized
Optimal Input Procurement
Managers should acquire inputs in such a way as to minimize costs which will depend on the extent to which there is a relationship specific exchange. - Spot exchange: if there are many buyers and sellers then price is set by the intersection of supply and demand and if a seller is selling at a higher price than the market, the buyer can simply go somewhere else. Downfalls: not protected by opportunism, bargaining and underinvestment in quality - Contract alleviates the need to have to bargain every time you need to purchase an input. Offers protection and guarantees an acceptable price for both parties or an extended time horizon and reduces the incentive for either the buyer or the seller to skimp on specialized investments required for the exchange - Biggest advantage when it comes to vertical integration is that it skips the middle man by producing its own inputs
Firms often pay managers a percent of profits to encourage them to work longer hours for the company. Managers are often conflicted by the desire for extra income and the reduction of leisure time for family and personal enjoyment. Consider the following example. When the manager is paid a salary of $100,000 without a share of profits, she spends the minimum required time at work and maximizes her leisure time. When the manager is paid $100,000 plus a small percent of profits she increases the time spent at work. Her average income increases to $120,000. Can you tell from this example whether the manager has shown a preference for the second compensation scheme? If so, has the company benefited from the second compensation scheme?
a. Scheme 1: manager is paid a salary of $100,000 w/out share of profits, min time spent at work Scheme 2: manager is paid $100,000 plus a percentage of profits as she increases time at work, average income increases to $120,000 The manager showed preference for the second scheme since her hours increased and she received an additional $20,000. If she had preferred scheme 1, you wouldn't have seen an increase in her average income and time spent at the office. The company would only have benefited from the increase in hours if their increase in revenues exceed the additional cost in labour. Say their revenues increased by $10,000 then having the employee stay longer hours represents a cost of $10,000 ($20,000-$10,000) to the company. If their revenues increased by $30,000 then they would have benefit $10,00 in additional revenue
Spot Exchange
an informal relationship between a buyer and seller in which neither party is obligated to adhere to specific terms for exchange
