# ECONOMICS A02Y - INTRODUCTORY ECONOMICS (A Mathematical Approach) - Download as DOC

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```							ECONOMICS A02Y - INTRODUCTORY ECONOMICS (A Mathematical
Approach)

Second Test: November 6, 2000 – Answers

1. The shutdown price is the one at which the firm’s average variable costs (avoidable
costs) and revenues are equal, in other words where price is equal to the minimum
average variable cost. AVC = 0.5q + 2 + 8q-1 and dAVC/dq = 0.5 – 8q-2. We can set
this derivative = 0 to find the output level at which AVC reaches its minimum. So, 0.5 –
8q-2 = 0, or q2 = 16, so q = 4. Substituting this value into the AVC function gives us
0.5(4) + 2 +32/4 = \$6. The correct answer is (F).

2. The firm will produce where MR = MC. For the perfectly competitive firm, the MR
function is a constant at the going price, MR = \$14. We can find the MC function as
dTC/dq = q + 2. Setting these two equal, we find q = 12. The correct answer is (L).

3. The firm will produce where MR = MC. For the perfectly competitive firm, the MR
function is a constant at the going price, MR = \$20. We can find the MC function as
dTC/dq = q + 2. Setting these two equal, we find q = 18. The firm therefore earns
revenue of 18 x \$20 = \$360. Total costs can be found with the total cost function as .5 x
18 x 18 + 2 x 18 + 32 = \$230. The firm therefore earns a profit of \$130 in each period.

4. The industry supply curve is the summation of the marginal cost curves of each of the
individual firms in the industry (above AVC). Since there are 200 firms in the industry in
the short run Q = 200q. The marginal cost curve (function) is the first derivative of the
total cost function: dTC/dq = q + 2. Since q = Q/200, the sum of the marginal costs is
given by (Q/200) + 2 = 0.005Q + 2. Therefore, the equation of the short run supply curve
for the industry is P = 2 + 0.005Q. The equilibrium quantity traded in the industry will
be where 32 - .01Q = 2 + 0.005Q. 0.015Q = 30, or Q* = 2000. The equilibrium price in
the industry will be \$12. At a price of \$12, the individual firm will profit-maximize by
producing where 12 = q + 2 (i.e., where MR = MC). q = 10. The correct answer is (J).

5. Since, in the long run, each perfectly competitive firm must be at the minimum point
on the long run average cost curve, we know that each firm in the long run will produce 8
units of output and sell it at \$10, the equation of the long run supply curve is P = \$10.
The total amount traded in the industry in the long run will be where 32 - .01Q = 10, or
where Q*LR = 2200. Since each firm will be producing 8 units of output, the number of
firms will be 2200/8 = 275. The correct answer is (W).

6. In the long run, each perfectly competitive firm must be at the minimum point on the
long run average cost curve, which is now at 13 units of output and at \$6. Therefore, the
equation of the new long run supply curve is P = \$6. The total amount traded in the
industry in the long run will be where 32 - .01Q = 6, or where Q*LR = 2600. Since each
firm will be producing 13 units of output, the number of firms will be 2600/13 = 200.
7. Since MR = MC, this firm is maximizing profit in the short run. It is not covering its
average costs (P < AC), but it is covering its average variable costs (P > AVC). So, the best
it can do in the short run is to keep output constant, and not shut down. The correct answer
is (C).

8. The optimal hiring rule is that the firm should continue to hire workers until the marginal
contribution of the firm to the revenues of the firm (the value of the marginal product) is just
equal to the marginal cost to the firm of hiring more labour (the wage of the worker). In
symbols VMPL = PL or MPL x PX = PL. Since, the marginal product of labour is dQ/dL = 48
– 0.2L, we can calculate (48 – 0.2L) x 10 = 20, or 480 – 2L = 20 or L = 230. The correct

9. The correct answer is (C).

10. Average variable costs are total variable costs/q and average fixed costs are TFC/q
and average costs are AVC + AFC. Doubling of wages will double total variable costs at
any level of q, so AVC will double. However, fixed costs are unaffected by a doubling of
wages, so AFC is not changed. Since AVC doubles but AFC is unchanged, AC will less

11. This is a perfectly competitive firm which is maximizing its profit since MR = MC.
The current price is above both average variable cost and average cost. Since both AVC
and AC reach their minimums as they cross the MC curve, and since the current level of
output must be greater than the outputs at which those minimums are reached, both AC
and AVC must be rising at the current level of output. If output increases by a little bit,
then AVC and AC will both still be rising. Average fixed cost is always falling as output
increases. Marginal cost will be rising as output increases. Therefore, (G) is the

12. The intercept of the short run industry supply curve is at P = 200. Another point on
the supply curve comes at P = 600, Q = 400. The slope is the rise/run, so this is (600 –
200)/400 = 1. So the equation of the short run supply curve for the industry is P = 200 +
1Q or P = 200 + Q. This industry supply curve is the sum of the marginal cost curves of
the 200 firms in the industry, so Q = 200q. We can substitute this into the industry
supply curve to get the marginal cost curve of each firm. P = 200 + 200q. The correct

13. Since the firms and the industry are in a short run equilibrium position, and there are
200 identical firms in the industry, we can find this by simply dividing the industry
output by the number of firms: 400/200 = 2. Alternatively, we could take the equilibrium
price of the output, which is \$600 and set it equal to the marginal cost function: 600 =
200 + 200q, so that q = 2. The correct answer is (B).

14. In the long run, each perfectly competitive firm must be at the minimum point on the
long run average cost curve, with costs of \$400 per unit of output . Since every firm
operates at this output and these costs, and in the long run firms will enter the industry
until the price is driven down to just equal average costs, and because this is a constant
cost industry, we can deduce that the equation of the long run industry supply curve is P
= \$400. The demand curve has a vertical intercept of 1000 and a negative slope of
1000/1000 = 1, so the equation of the demand curve is P = 1000 – Q. Putting demand
and supply together, we have 1000 – Q = 400, so that Q = 600. This is the long run
output of the industry. Answer (F) is correct.

15. In the long run, firms in a perfectly competitive industry will necessarily earn zero
profit in the long run. This occurs because, in the long run, firms can and will enter or
exit the industry as long as returns in this industry are above or below normal returns
available in other industries. Firms stop entering and exiting when the economic profit is
equal to zero (i.e., firms are earning a normal level of return). The correct answer is
(Y).

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