Eco 207
Spring 2007
Exam 2
250 points
Please answer all of the following questions carefully and completely, being sure to explain completely and to label everything carefully. Show your work, where appropriate. 20% credit for completely blank answers; no credit for sufficiently bad answers.
1. Consider a firm that, in the short run, has diminishing marginal returns at every level of output. On the graphs below, show the approximate shapes of the total product, marginal product, average product, total cost, marginal cost, average variable cost, and average total cost curves. (35 points) BE SURE TO LABEL EVERYTHING.
See graphs in separate file.
4 points each curve (total of 28)
Correct labeling of axis on each graph (3 points)
TC starts at FC (any point above the origin) (2 points)
ATC=MC at minimum ATC (2 points)
Graphs must be logically consistent with each other.
2. A firm has the production function Q = K1/2L1/2, and is currently using 400 units of labor and 400 units of capital. The wage rate and the rental rate on capital are both $20. The expansion path for this firm is K=L.
a. Draw an isoquant map showing the current production of the firm and the isocost curve on which the firm is currently producing. Carefully label EVERYTHING. What quantity is the firm producing, and what is the total cost of the firm at this moment? (20 points)
See graphs in separate file.
Current production is Q = 400 (3 points).
TC = 20(400) + 20(400) = $16,000 (3 points)
Graph points: Total of 14 (out of total 20 for this question)
Label on each axis (1)
Appropriate shape of isoquant (3)
Appropriate shape of isocost (3)
Tangent at (400, 400) (3)
Correct labeling (4)
b. Suppose that in the short run, the firm wishes to DEcrease its production to 100. Draw a NEW isoquant map showing (1) the position you showed in (a), (2) how the firm would decrease production in the short run, and the related cost, and (3) how the firm would decrease production in the long run, and the related cost. (30 points)
See graphs in separate file.
In the short run, K is fixed at 400. Thus 100 = 20L1/2; solve for L to get L=25. (4 points)
STC = 20(25) + 20(400) = $8,500. (4 points)
In the long run, the firm would decrease production along the expansion path.
K=L=100 (4 points)
TC = $4,000. (4 points)
Graph points: (14 out of total 30 points)
Note that graph should contain original point from a.
Short run point: ON original isoquant (3)
On new, higher isocost curve that is NOT tangent (3)
Labeling (1)
Long run point:
On NEW isoquant (2)
On NEW isocost (2)
Tangent (2)
Labeling (1)
c. Using your results for b., draw a graph of the approximate shape of the firm’s short and long-run total cost curves as a function of Q. (15 points)
See graphs in separate file. 5 points for each correct curve.
Mathematical work shown here can carry over to the extra credit question, but is not necessary for this question, and is not a complete answer to the extra credit problem.
3. Consider a perfectly-competitive, constant-cost industry.
Demand in this industry is given by:
QD = 3000 – 30P
There are an unlimited number of identical firms with the following cost curve:
TC = q2 + 10q + 400
MC = 2q + 10
a. Find the long-run equilibrium price, quantity, and number of firms. (15 points)
ATC=q + 10 + 400/q
q + 10 + 400/q = 2q + 10
q = 20, P = $50
(3 pts for ATC, 3 pts each for P and Q)
Q = 3000 – 30(50) = 1500 (3 pts)
1500/20 = 75 = number of firms (3 pts)
b. Find the equation of the short-run supply curve based on the number of firms in long-run equilibrium. (Round number of firms to the nearest whole number.) (10 points)
MC = 2q + 10
P = 2q + 10
q = -5 + 1/2P
Q = -375 + 75/2 P (or -375 + 37.5 P) (or P = 10 + 2/75 Q or P = 10 + 0.03Q)
(5 pts method, 5 pts answer)
c. Now suppose that demand increases to Q = 4000 – 30P. Calculate the short-run and long-run prices and quantities and number of firms. Use these results in your graphs and explanation be on the next page. (20 points)
Long run: q=20, P= $50, so Q = 4000 – 30(50) = 2,500 (7 pts)
Number of firms = 2500/20 = 125 (3 pts)
Short run: set SR supply equal to new demand.
-375 + 75/2 P = 4,000 – 30P
P = $64.81, Q = 2,056 (rounded to nearest whole number) (7 pts)
q= 2056/75 = 27 (rounded) (or you could find this by plugging price into MC) (3 pts)
d. Carefully graph your results. You should have a graph for the industry, a graph for the firm, and you should show all short and long-run points that you found in a, b, and c. EXPLAIN carefully what has happened in this industry in the short and long run. (35 points)
EXPLANATION: (15 points)
Short run: The increase in demand causes industry price and output to increase (along the SR supply curve).(2) Existing firms produce more (2) and make a positive profit. (2)
Long run: More firms enter. (3) This causes price to fall (2) and quantity to increase (2) until profit returns to zero. (2) (In the new long-run equilibrium, there will be more firms, but each firm will produce exactly the breakeven quantity and make a profit of zero.)
GRAPHS: (20 points, 10 points each graph)
See separate file.
4. In class, we discussed the different effects of lump-sum versus sales taxes in the short and long run. Carefully explain, with use of graphs, why the type of the tax determines who pays it in the short run, but in the long run (in perfectly competitive, constant cost industries), all taxes are passed on to consumers. (30 points)
(Note: You do NOT need to explain every step of what happens in each industry/firm with each type of tax, but you DO need to have enough of an explanation and graphs of AT LEAST the industries to fully explain your answer.)
The answer to this question MUST indicate that:
1. In the short run, the effects of these taxes are different. There is no effect on Q and P with a lump-sum tax; firms will just lose money. With a sales tax, consumers and producers share the burden depending on the relative elasticities of demand. (15 points)
2. In the long run, the effects of these taxes are essentially identical; in both cases, the full amount of the tax is passed on to consumers, since firms will exit as long as they are not breaking even.
(15 points)
To receive full credit, there MUST be some graphical explanation that clearly supports the story above.
5. Identify whether each of the following statements is TRUE, FALSE, or UNCERTAIN, and explain your answer. (Note: you are getting credit for the explanation, not the t/f/u part. Answers with no explanation will receive no credit. Use graphs to support your answers where appropriate. Your answers should explain WHY the statement is tr/f/u and define all relevant terms.)
a. A firm that experiences diminishing marginal returns in the short run will have decreasing returns to scale in the long run.
FALSE OR UNCERTAIN. These concepts are unrelated. Diminishing returns refers to declining MP in the short run, the result of the increasing scarcity of the fixed input (capital). Diseconomies of scale refers to rising long-run average cost, due to either decreasing returns to scale or other coordination problems. All firms have diminishing returns in the short run. This is unconnected to whether there are diseconomies in the long run.
b. If a firm is a price taker, it must set the same price as every other firm. (10 points)
T or F or U. If the firm is a price taker, it has no ability to set a price different from other firms. This means that if the firm sets a higher price, no one will buy the product, and if the firm sets a lower price, it will simply lose money. Thus while it CAN set any price it chooses, it would not be a profit-maximizing choice to do so.
c. If short run marginal cost is increasing, short run average total cost must be increasing too.
False or uncertain. If SMC is increasing, then SATC might be increasing or decreasing. This can easily be shown graphically.
d. Diminishing returns occurs because you always hire the best workers first, so new workers are less productive.
False. Diminishing returns (or diminishing marginal returns) occurs because, in the short run, capital is fixed. Thus you are adding more and more variable inputs to a fixed input, and capital per worker is getting scarce. Each worker is less productive than the last one because he has less capital to work with.
e. A firm that is making an economic profit of zero would be better off exiting the industry and doing something else.
False. Zero economic profit means that the firm’s revenue is covering explicit costs plus opportunity costs. Since opportunity cost represents the value of the firm’s assets in its next best choice, the firm would earn exactly the same amount in its next best choice. Thus it would be no better off exiting the industry.
EXTRA CREDIT
Possible 10 points
(no credit for blank answers)
Refer to the firm describes in 2a. Derive the precise mathematical form of the firm’s short run and long run cost curves (TC, MC, ATC, AVC where appropriate) and graph them. Assume that K = 400.
Long run curves: the expansion path is K=L, so each unit costs $40.
LTC = 40Q
LMC = 40
LAC = 40
(1 point each)
Short run curves:
STC = 20L + 20(400)
=20L + 8000
From production function, Q = 20L1/2 , or L = Q2/20
Thus STC = Q2 + 8000
MC = 2Q
ATC = 2Q + 8000/Q
AVC = Q
(1 points each)
See graphs in separate file.
Graphs MUST have the right shapes.
(3 points for correct graph of AVC, MC, ATC, etc.)