Econ 100a: Ch. 7
You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q=5KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r=$20,000 per week, and each team costs w=$4,000 per week. Engine costs are given by the cost of labor teams and machines, plus $5,000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. The total cost of producing q units of output (TC) is
TC = 100,000 + 4,000 (q/25) + 5000q
A firm has a fixed production cost of $1,000 and a constant marginal cost of production of $200 per unit produced. What is the firm's total cost function?
TC = 1000 + (200q)
Sunk cost
expenditure that has been made and cannot be recovered - sunk cost should always be ignored when making future economic decisions -b/c it has no alternative use, its opportunity cost is zero
The graph shows long-run costs for a firm. If the firm produces ______ units, it will experience _____.
more than 9000; diseconomies of scale because managing larger firms results in higher costs
Economies of scale
when a firm increases its output and the average cost of production falls, there are economies of scale
Economies of scale
when doubling of output is achieved with less than doubling of cost
Increasing returns to scale
when output more than doubles with the doubling of all the inputs
Is the firm's expansion path always a straight line? A firm's expansion path
will not be a straight line if the ratio of inputs used changes with output
Diseconomies of scale can happen for the following reasons:
- At least in the short run, factory space and machinery may make it more difficult for workers to do their jobs effectively - Managing a larger firm may become more complex and inefficient as the number of tasks increases - The advantages of buying in bulk may have disappeared once certain quantities are reached. At some point, available supplies of key inputs may be limited, pushing their costs up
Measurement of economies of scale
- Economies of scale are often measured in terms of a cost-output elasticity, Ec
Economies of scale can happen for the following reasons:
- at a larger scale, workers can get specialized in the activities at which they are most productive - by varying the combination of inputs utilized to produce the firm's output, managers can organize the production process more effectively - The firm may be able to acquire some production inputs at lower cost because it is buying them in large quantities and thus can negotiate -Economies of scale: AC of production falls as the output level increases
choosing cost-minimizing inputs
- if firm wants to produce a given level of output, then the cost-minimizing combinations of inputs is shown by the tangency pt - at pt of cost minimization, marginal rate of tech. sub. = input price ratio
cost in the long-run
- in the long run, firm can expand its capacity by expanding existing factories or building new ones; it can expand or contract its machinery equipment etc. - in the long run there are no fixed costs, all costs are variable - a firm thus has the flexibility of choosing its combination of inputs so that it can produce a given output at the lowest cost possible
long run average cost curve
- long run average cost curve (LAC) shows the average cost of producing a given level of output in the long-run, when no inputs are fixed LAC is the envelope of the short run average cost curves - if there are many choices of plant size, each having a different short-run average cost curve, then the firm can choose the plant size that allows it to produce that output at the minimum average cost - LMC is not the envelope of the short-run marginal cost - LMC shows the change in the long-run cost as output is increasing by 1 unit - each pt on the long-run marginal cost is the short run mc associated with the most cost efficient plant
Production with perfect complements
- when inputs are perfect complements, then the production function has L-shaped isoquants - this means that each level of output requires a specific combination of labor and capital - to increase output, both the inputs must be increased proportionally - such a production function is called the fixed-proportions or Leontief production function
Product with perfect substitutes
- when inputs are perfect substitutes for one another, then the isoquants are straight lines - The MRTS is constant at all points on an isoquant
The cost of flying a passenger plane from point A to point B is $60,000. 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. 1. The average cost per passenger for rush-hour flights (the first and last flights) is 2. The average cost per passenger for off-peak flights (the middle two flights) is 3. 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 or the rush-hour customer. What advice would you offer?
1. AC = 60000/240 = 250 2. AC = 60000/120 = 500 3. You should advise the airline to try attracting more customers during off peak times
Joe quits his computer programming job, where he was earning a salary of $65,000 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, $35,000; rent, $0; and other expenses, $35,000. Find the accounting cost and the economic cost associated with Joe's computer software business. (Enter numeric responses using an integer.) The accounting cost of joe's business is
124000
A firm has a fixed production cost of $1,000 and a constant marginal cost of production of $200 per unit produced. The firm's average total cost (ATC) of production is
ATC = (1000 + (200q))/q
Fred quits his job with a big accounting firm, where he was earning $85,000 per year, to start his own accounting business in a building he owns. He previously rented the building to someone who paid him rent of $22,000 per year, but now Fred collects no rent because he is using the building himself. Fred pays himself a salary of $35,000 per year and has other expenses of $29,000 per year. The yearly economic cost for Fred's accounting business is $enter your response here. (Enter your response as an integer.)
136000
A firm's long-run average cost (LAC) curve is downward sloping. Each short-run average cost (SAC) curve will be tangent to the LAC curve at
A point to the left of the minimum of the SAC curve
You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q=5KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r=$20,000 per week, and each team costs w=$4,000 per week. Engine costs are given by the cost of labor teams and machines, plus $5,000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. The average cost (AC) of producing q machines is
AC = 100,000/q + 5160
relationship between marginal cost and average cost: When MC < AC
AC falls
relationship between marginal cost and average cost: When MC = AC
AC is at the lowest point
relationship between marginal cost and average cost:When MC > AC
AC rises
User cost of capital
Annual of owning and using a capital asset, equal to economic depreciation plus forgone interest - Capital is often rented rather than purchased - If the capital market is competitive, the rental rate should be equal to the user cost, r - W is the wage rate, or the price of labor
Diseconomies of scale
At some point however, it is likely that the average cost of production will begin to increase with output - AC of production increases as the output level increases
You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q=5KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r=$20,000 per week, and each team costs w=$4,000 per week. Engine costs are given by the cost of labor teams and machines, plus $5,000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. The marginal cost (MC) of producing q machines is
MC = 5160
Suppose that a paving company produces paved parking spaces (q) using a fixed quantity of land (T) and variable quantities of cement (C) and labor (L). The firm is currently paving 1,000 parking spaces. The firm's cost of cement is $12.50 per acre covered (c) and its cost of labor is $35.00/hour (w). For the quantities of C and L that the firm haschosen, MPC=50 and MPL=7. is this firm minimizing its cost of producing parking spaces?
No since (MPL/w) does not equal (MPC/c)
Long-run average cost curve
The long-run average cost curve (LAC) shows the average cost of producing a given level of output in the long-run, when no inputs are fixed. LAC is the envelope of the short-run average cost curves
Economies of scale and increasing returns to scale
This implies that whenever there are increasing returns to scale, there are economies of scale - But economies of scale is more general, it applies even when the input proportion is changed as a firm changes its level of production
A recent issue of Business Week reported the following: During the recent auto sales slump, GM, Ford, and Chrysler decided it was cheaper to sell cars to rental companies at a loss than to lay off workers. That's because closing and reopening plants is expensive, partly because the automakers' current union contracts obligate them to pay many workers even if they're not working. When the article discusses selling cars "at a loss," is it referring to accounting profit or economic profit? How will the two differ in this case? Explain briefly. The article is referring to
accounting profit, which includes the sunk cost of the workers and is therefore lower than economic profit
MPk/r
additional output that results from spending additional dollar for capital
MPL/w
additional outputs that results from spending an additional dollar for labor
A product transformation curve shows
all combinations of two different products that can be produced with a given set of inputs
expansion paths
as a firm expands output, the cost of production increases/ every new level of output will be produced at a new possible cost-minimizing combinations of the inputs - joining these cost-minimizing points gives the firm's expansion path - the firm's long-run expansion path is straight line from the origin derived by joining the tangency points - in the short-run, however, as the capital is fixed, the firm faces the inflexibility of substituting capital for labor. The firm can increase output only by expanding labor, leading to a higher cost of production of the same output as in the long-run - thus, the firm's short-run expansion path begins as a line from the origin and then becomes horizontal when the capital input reaches the highest (fixed) level
In the long run, constant returns to scale necessarily occur when the firm increases its production and the firm's
average total cost does not change
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? The average variable cost curve will achieve its minimum at a lower level of output than the average total cost curve because
average total cost equals average variable cost plus average fixed cost, and the average fixed cost curve continues to fall as more output is produced
Assume that the marginal cost of production is less than the average variable cost. Can you determine whether the average variable cost is increasing or decreasing? Explain. If the marginal cost of production is less than the average variable cost of production, then
average variable cost is falling because the cost of the last unit produced is adding less to total variable cost than previous units did on average
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. If the marginal cost of production is greater than the average variable cost of production, then
average variable cost is rising because the cost of the last unit produced is adding more to total variable cost than previous units did on average
Total cost
cost of all inputs a firm uses in production TC = TFC + TVC 1) Divide equation 1 by Q, we get: TC/Q = (TFC/Q) + (TVC/Q) 2) ATC (average total cost) = AFC (average fixed cost) + AVC (average variable cost)
total variable cost
cost that changes as output changes (EX: labor costs, costs of raw materials used for production, etc)
total fixed cost
cost that remains constant as output changes (ex: lease payment for factory space, insurance costs, costs of plant maintenance, perhaps a minimal number of employees)
economic cost
cost to a firm of utilizing economic resources in production
Economic cost
cost to a firm of utilizing economic resources in production economic cost = opportunity cost
Why are isocost lines straight lines? Isocost lines are straight because the slope of such lines ___________________.
equals the ratio of input prices, and this ratio is fixed
You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q=5KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r=$20,000 per week, and each team costs w=$4,000 per week. Engine costs are given by the cost of labor teams and machines, plus $5,000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. How do average costs vary with output? as quantity increases, average costs
decrease
if a firm enjoys economies of scale up to a certain output level, and cost then increases proportionally with output, what can you say about the shape of the long-run average cost curve? The long-run average cost curve
decreases initially and then is horizontal
What is the difference between economies of scale and returns to scale?
economies of scale define how cost changes with output, and returns to scale define how output changes with input usage
There is no direct relationship between economies of scale and economies of scope because
economies of scale pertain to one output and economies of scope pertain to more than one output
A firm produces two products, X and Y. The product transformation curve for these two products is Y=40−0.1X2, where X is the number of units of product X and Y is the number of units of product Y produced in one day. The firm can produce no units of X and 40 units of Y or 20 units of X and no units of Y or various combinations of X and Y between these extremes. We can conclude from the product transformation curve that this firm faces ▼ economies of scope diseconomies of scope increasing returns to scale decreasing returns to scale .
economies of scope
Firm 1 produces product A only, and firm 2 produces product B only. Firm 3 produces the same amount of A as firm 1 AND the same amount of B as firm 2. All three firms use state-of-the-art production techniques, but firm 3's total costs are less than the sum of the other two firms' total costs. We can conclude that there are
economies of scope in producing products A and B
If a firm hires a currently unemployed worker, the opportunity cost of utilizing the worker's services is zero. This statement is
false because the workers time otherwise spent in leisure activities has value
Economies of scale can occur as a result of which of the following?
greater specialization of labor and capital as the firm increases its size
Returns to scale
if a firm expands the scale of operation by increasing all the inputs proportionately, then the change
choosing the cost-minimizing inputs
if the firm wants to produce a given level of output, then the cost-minimizing combination of inputs is shown by the tangency point - at the point of cost-minimization, marginal rate of technical substitution = input price ratio
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? and the average cost of production will
increase
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? the marginal cost of production will
increase
Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. How does this tax affect the firm's fixed, marginal, and average costs? With a lump-sum tax, the fixed cost of production will
increase
Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. How does this tax affect the firm's fixed, marginal, and average costs? and the average cost of production will
increase
A firm pays its accountant an annual retainer of $20,000. Is this an economic cost? The annual retainer:
is an economic cost because it is an explicit cost
Suppose that labor is the only variable input to the production process. If the marginal cost of production is increasing as more units of output are produced, what can you say about the marginal product of labor? If the marginal cost of production is increasing as more units of output are produced, then the marginal product of labor
is diminishing
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? If the marginal cost of production is diminishing as more units of output are produced, then the marginal product of labor
is increasing
A chair manufacturer hires its assembly-line labor for $20 an hour and calculates that the rental cost of its machinery is $5 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 2 hours of labor for every two hours of machine time, is it minimizing its cost ofproduction? If so, why? If not, how can it improve thesituation? The firm
is not currently minimizing its cost of production because the marginal product of labor divided by the wage is less than the marginal product of capital divided by the rental cost
marginal cost
is the change in total cost as another unit of output is produced
opportunity cost
is the cost associated with opportunities forgone when a firm's resources are not put to their best alternative use
Ec
is the percentage change in the cost of production resulting from a 1-percent increase in output: Ec = (△C/C)/(△q/q) or Ec = (△C/△q) / (C/q) = MC/AC
isocost line
isocost line shows all the combinations of two inputs, such as capital and labor, that have the same cost The equation of the isocost line can be written as: C = wL + rK - slope of the line is given by △K/△L = -w/r - The slope shows how many units of capital could be replaced by a unit of labor with no change of total cost
cost minimizing firm should choose
its quantities of inputs so that the last dollars worth of any input added to the production process yields the same amount of extra output
Suppose a chair manufacturer finds that the marginal rate of technical substitution (MRTS) of capital for labor in her production process is substantially less than the ratio of the wage rate for assembly-line labor (w) to the rental rate on machinery (r). How should she alter her use of labor and capital to minimize the cost of production? holding output constant, the chair manufacturer should use _____ labor and _____ capital
less, more
A firm's long−run average cost curve shows the ________ average cost at which it is possible to produce each output when the firm has had ________ time to change both its labor force and its plant.
lowest; sufficient
Suppose a chair manufacturer finds that the marginal rate of technical substitution (MRTS) of capital for labor in her production process is substantially greater than the ratio of the wage rate for assembly-line labor (w) to the rental rate on machinery (r). How should she alter her use of labor and capital to minimize the cost of production? holding output constant, the chair manufacturer should use _____ labor and _____ capital
more, less
Jose rents office space for $20,000 per year. He uses the office to fill out tax returns for 1,000 clients per year. If the office rent increases to $25,000 per year, the marginal cost of filling out tax returns will
not change
economic cost =
opportunity cost -
Distinguish between economies of scale and economies of scope. Why can one be present without the other? Economies of scale occur when
output can be doubled for less than a doubling of cost; however, economies of scope occur when joint output is less costly than the sum of the costs of producing multiple outputs separately
average cost
per unit of production
Assume that the marginal cost (MC) of production is decreasing. Can you determine whether the average variable cost(AVC) is increasing or decreasing? Explain.
regardless of whether MC is decreasing, AVC could be increasing or decreasing depending on whether MC is greater than or less than AVC
Assume that the marginal cost (MC) of production is increasing. Can you determine whether the average variable cost(AVC) is increasing or decreasing? Explain.
regardless of whether MC is increasing, AVC could be increasing or decreasing depending on whether MC is greater than or less than AVC
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? With a proportional tax, the fixed cost of production will
remains unchanged
Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. How does this tax affect the firm's fixed, marginal, and average costs? the marginal cost of production will
remains unchanged
The long run average cost curve
shows the lowest average cost facing a firm as it increases output changing both its plant and labor force
How does a change in the price of one input change the firm's long-run expansion path? If the price of an input changes, then the
slope of the isocost lines will change, and the firm will substitute toward the relatively expensive input, pivoting the expansion path toward the axis of the relatively cheaper input
The owner of a small retail store does her own accounting work. How would you measure the opportunity cost of herwork? The opportunity cost of the owner's accounting work is
the monetary amount that her time would have been worth in its next best use
Cost curves
the total cost and total variable cost increase as more output is produced. The total fixed cost is constant for any level of output - the marginal cost, average total cost and average variable cost curves first fall and then rise. The marginal cost curve intersects the average total cost and average variable cost curves at their minimum points - average fixed cost falls continuously as more output is produced
Returns to scale: if the output increases by the same proportion
then there are constant returns to scale
Returns to scale: if the output increases by a lower proportion
then there are decreasing returns to scale
Returns to scale: if the output increases by a higher proportion
then there are increasing returns to scale
in the short run when some inputs are fixed, marginal cost must eventually rise as a firm's output increases because
there will eventually be diminishing marginal products for the firms variable inputs
If the owner of a business pays himself no salary, then the accounting cost is zero, but the economic cost is positive. This statement is
true because economic costs include opportunity costs such as the value of the business owner's time
A firm that has positive accounting profit does not necessarily have positive economic profit. This statement is
true, because economic costs will be greater than accounting costs if implicit costs exist
A firm uses 80 hours of labor and 6 units of capital to produce 10,000 gadgets per day. Labor's marginal product is 4 gadgets per hour and the marginal product of capital is 20 gadgets per unit. Each unit of labor costs $8 per hour and each unit of capital costs $50 per unit. If the firm wants to continue producing 10,000 gadgets per day at the lowest possible cost, it should
use more labor and less capital
A firm has a fixed production cost of $1,000 and a constant marginal cost of production of $200 per unit produced. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.
very large b/c the average total cost of production falls with output
input substitution
what should a firm do if an input price changes? - if labor becomes cheaper, then the firm can substitute labor for capital to minimal cost
Ec < 1
when MC < AC (costs increase less than proportionately with output, economies of scale)
Ec = 1
when MC = AC (cost increase proportionately with output, neither economies nor diseconomies of scale) - neither economies or diseconomies of scale (constant returns to scale would apply if input proportions are fixed)
Ec > 1
when MC > AC (costs increase more than proportionately with output, diseconomies of scale)
Suppose that a paving company produces paved parking spaces (q) using a fixed quantity of land (T) and variable quantities of cement (C) and labor (L). The firm is currently paving 1,000 parking spaces. The firm's cost of cement is $12.50 per acre covered (c) and its cost of labor is $35.00/hour (w). For the quantities of C and L that the firm haschosen, MPC=50 and MPL=7. Does the firm need to alter its choices of C and L to decrease cost?
yes, they need to increase C which would cause MPL to increase and MPC to decrease
