Download November 7, 2003

Answers to Second Test, ECMA04H, November 7, 2003
1. If q = 10L1/3, then the marginal product of labour is dq/dL = 10 x 1/3 L-2/3. At L = 8, this is
10/12 = 0.833 or 5/6. The correct answer is (C).
2. The marginal cost per unit of output is given by the price of an extra unit of labour divided by
the marginal product of that labour. In this case, this is 4/(10/3 L-2/3), evaluated at L = 125.
This is 4/(10/75), which is $30. The correct answer is (O).
3. The total cost function is given by the price of capital times the number of units of capital
employed, plus the price of labour times the number of units of labour. This is (27 x 8) + (4 x
L). The average cost function is TC/q, where q = 10L1/3, so AC = 216/(10L1/3) +
(4L)/(10L1/3). This can be written as 21.6 L-1/3 + 0.4L2/3. Taking the derivative of AC with
respect to L, we have dAC/dL = -7.2L-4/3 + 4/15 L-1/3. Setting this derivative equal to zero,
we have L4/3 / L1/3 = (15 x 7.2)/4 or L = 27. The correct answer is (M).
4. TC = 2q2 + 100q + 200 and FC = 72. We know that TC = VC + FC, so AC = AVC + AFC, or
AFC = AC – AVC. When q = 144, AFC = 72/144 = $0.50. In other words, the difference
between AC and AVC is $0.50. The correct answer is (D).
5. TC = 2q2 + 100q + 200 so AC = 2q + 100 + 200q-1. dAC/dq = 2 – 200q-2, which we can set
equal to zero to find the minimum. If 2 – 200q-2 = 0, then q2 = 100, or q = 10. At q = 10, AC
= (2 x 10) + 100 + 200/10 = $140. The correct answer is (O).
6. If P = 128, firms will profit maximize by setting P = MC. MC = 4q + 100, so 128 = 4q +
100, or q = 7. At this output, profit can be found as TR – TC = (128 x 7) – [(2 x 7 x 7) + (100
x 7) + 200] = 896 – 998 = -$102. This is the best the firm could do while continuing to
operate, but it involves a loss which is larger than the amount of fixed costs. In other words,
the firm is not even covering its variable costs by operating, and therefore, in the short run, it
will make more sense for this firm to shut down and produce zero output. In that case, the
firm’s loss will be equal to fixed costs, which is $72. The correct answer is (D).
7. The correct answer is (C).
8. AC = AFC + AVC and AFC = FC/q. If FC rises by 20%, then AFC will rise by 20%, but AC
will rise by less than 20% (because variable costs do not rise). The correct answer is (D).
9. Marginal cost is equal to the price of one more unit of labour divided by the marginal output
produced by that labour (marginal product of labour), so marginal cost is inversely related to
marginal product of labour (not to the average product of labour). It is average variable cost
which is inversely related to the average product of labour. The correct answer is (B).
10. TC = 4q2 + 24q + 576, with FC = 320. Therefore, VC = 4q2 + 24q + 256 and AVC = 4q + 24
+ 256q-1. dAVC/dq = 4 – 256q-2 = 0, or q2 = 256/4 or q = 8. Evaluating AVC at q = 8, we
have (4 x 8) + 24 + (256/8) = $88. The firm will shut down if it is unable to at least cover its
variable costs, so it will shut down if the price is below $88. The correct answer is (K).
11. In the short run, P = MC is the profit maximizing rule and MC = 8q + 24. So 160 = 8q + 24
or q = 17. The correct answer is (G).
12. Profit = TR – TC = (160 x 17) – [(4 x 17 x 17) + (24 x 17) + 576] = 2720 – 2140 = $580.
The correct answer is (N).
13. Marginal cost = dTC/dq = 8q + 24. The supply curve of the individual perfectly competitive
firm is MC above AVC, so is given by P = 24 + 8q, for all q 17. There are 100 identical
firms, so 100q = Q or q = .01Q. By substitution, we can find the supply curve for the entire
industry in the short run, which is P = 24 + .08Q, for Q  1700. The find the equilibrium
quantity traded in the industry set demand equal to supply: 393 - .125Q = 24 +.08Q or 369 =
.205Q, or Q = 1800. Since there are 100 identical firms in the industry, that means that each
firm produces 18 units. The correct answer is (H).
14. When Q = 1800, the equilibrium price is P = 393 - .125(1800) = $168. Profit for each firm
will be TR – TC, which is (168 x 18) – [(4 x 18 x 18) + (24 x 18) + 576] = 3024 –2304 =
$720. The correct answer is (S).
15. This is a constant cost industry in which the minimum LRAC occurs at q = 12. At q = 12,
LRAC = 4q + 24 + 576q-1 = (4 x 12) + 24 + 576/12 = $120. Since each firm in long run
equilibrium produces at minimum LRAC, and since input costs do not rise as output of the
constant cost industry expands, the equation of the long run supply curve for the industry is P
= 120. Demand is P = 393 - .125Q, so we have 393 - .125Q = 120, so the long run
equilibrium output in the industry is 2184. Since each firm produces 12 units in long run
equilibrium, there are 2184/12 = 182 firms in the industry in the long run (i.e., 82 firms have
entered). The correct answer is (M).
16. In long run equilibrium each firm necessarily earns zero profit. The correct answer is (A).
17. Statements I and II are correct, but statement III contradicts statement II, so is incorrect. The
correct answer is (D).
18. Statement I is not correct (MC = MR yields maximum profit). Statement II is not correct for
the short run. Statement III is correct. The correct answer is (C).
19. Statements I and IV are correct. The correct answer is (G).
20. At the current output, P > MC, which means that output needs to rise to get to the profit
maximizing equilibrium of P = MC. The correct answer is (D).
21. The MC curve cuts through the minimum point of both AVC and AC. Since at the current
level of output, AC > MC, AC is falling (MC is “pulling the AC curve down”). At current
output, MC > AVC, so AVC is rising (MC is “pulling the AVC curve up”). MC is positively
sloped. The correct answer is (A).
22. TC = 2q2 + 60q + 450 and FC = 112. MC = dTC/dq = 4q + 60. P = MC, so 180 = 4q + 60,
so q = 30. Profit = TR – TC = (180 x 30) – [(2 x 30 x 30) + (60 x 30) + 450] = 5400 – 4500 =
$1350. The correct answer is (Q).
23. VC = 2q2 + 60q + 338. VC’ = 1.5(2q2 + 60q + 338) = 3q2 + 90q + 507. MC = 4q + 60 and
MC’ = 6q + 90. At P = $180, the firm profit maximizes where 180 = 6q + 90, or q* = 15.
Profit will be (180 x 15) – [3q2 + 90q + 507 + 112] = (180 x 15) – [(3 x 15 x 15) + (90 x 15)
+ 619] = 2700 – 2644 = $56. The correct answer is (B).
24. FC’ = $168. TC’ = 2q2 + 60q + 506. MC = 4q + 60 and P = $180, so q* is unchanged from
question 22 at q = 30. Profit = (180 x 30) – [(2 x 30 x 30) + (60 x 30) + 506] = 5400 – 4106
= $1294. The correct answer is (P).
25. AVC stays the same and AC rises relative to AVC. The minimum of the new AC must still
be at MC (which hasn’t changed) and therefore the minimum of the new AC must be to the
right of its former position along the positively sloped MC curve (higher output). The correct
answer is (C).