Download Test answers - November 4, 2002

ECONOMICS A02Y - INTRODUCTORY ECONOMICS (A Mathematical Approach)
First Test: November 4, 2002 -- Answers
MULTIPLE CHOICE ANSWERS
1. The substantial fall in consumer incomes will shift the demand curve for macaroni (a normal
good) to the left. Spaghetti is a substitute in consumption for macaroni, so a fall in the price of
spaghetti will decrease the demand for macaroni (shift demand curve to left). Both of these shifts
operate in the same direction, so the net effect is to decrease the price and quantity traded of
macaroni. The correct answer is (C).
2. The rise in the wage rate of macaroni workers will shift the supply of macaroni to the left.
Since cheese sauce is a complement in consumption to macaroni, a rise in the price of cheese
sauce will shift the demand for macaroni to the left. The net effect of these two events will be to
decrease output, but it is not possible to tell whether equilibrium price will rise or fall, without
knowing the size of impact of these two events. The correct answer is (F).
3. The tax on spaghetti will raise its price. Since spaghetti is a substitute in consumption for
macaroni, this price increase will increase the demand for macaroni (shift it to the right). The fall
in the price of macaroni-shaped candy (a substitute in production for macaroni) will encourage
producers to switch towards the production of macaroni, so the supply curve for macaroni will
shift to the right. The net effect of these two events will be to increase the output of macaroni,
but it is not possible to tell whether equilibrium price will rise or fall, without knowing the size
of impact of these two events. The correct answer is (E).
4. The diagram shows a demand curve with vertical intercept at 100 and horizontal intercept at
1000. Point AA@ is on the demand curve at P = 80. The equation of the demand curve, which is
linear, will be P = 100 – 0.1Q. Substituting into this equation, we can figure that point AA@ is at
P = 80, Q = 200. The elasticity of demand at this point will be given by dQ/dP  P/Q = 1/0.1  80/200 = 4.
The correct answer is (O).
5. Since demand is elastic at point AA@, the percentage change in quantity demanded will be
larger than the percentage change in price (for small changes in price). If price falls by a small
amount, quantity will increase but by a larger percentage amount. Total expenditure (price x
quantity) on toothpicks will therefore rise. The correct answer is (B).
6. The second derivative of this equation of the PPF is -22. The negative sign indicates that the
PPF is bowed outwards from the origin, so there are increasing costs of producing more X. The
correct answer is (C).
7. The demand curve of the monopolist is P = b - aQ. Total revenue is maximized when
marginal revenue equals zero. Marginal revenue is MR = b - 2aQ. When b - 2aQ = 0, Q =
b/(2a). The correct answer is (D).
8. If U = 3X2/3 , then marginal utility = dU/dX = 2X-1/3 . Consumers will follow the optimal
purchase rule in making their purchasing decisions, which implies $0.10 = 2X-1/3 . This means
that the consumer will purchase 8000 units of X. The correct answer is (P).
9. If the price of electricity is $0.10, then $0.10 = 2X-1/3. This means that the optimal value of X
is 8000. The total amount of consumer surplus is given by (Total Utility - PXX) = 3X2/3 - PXX =
$1200 - $0.10  8000 = $1200 - $800 = $400. The correct answer is (J).
10. Since P = MR, this must be a perfectly competitive firm. Since, at the current quantity of
output AC = MC, the firm must be producing the quantity which will give it minimum average
costs in the short run (and also in the long run, given what we are told in the question). Currently
the firm is earning higher revenues than its average costs or average variable costs, but it is not
producing the output which will maximize its profits. This firm should increase its output to
reach the point where MC = MR, where it will earn maximum profits.. The correct answer is
(F).
11. A firm will shut down if it can=t cover its average variable costs in the short run. TVC = TC
- FC = 400 + 10q + q2 - 300 = 100 + 10q + q2. Therefore, AVC = 100/q + 10 + q. AVC reaches
its minimum where dAVC/dq = 0. dAVC/dq = 1 - 100q-2 = 0. Therefore at q = 10, AVC reaches
its minimum. When q = 10, AVC = 100/10 + 10 + 10 = $30. The correct answer is (K).
12. When the government imposes a tax of $8 per textbook on producers, this will shift up the
marginal cost curve vertically by $8. MC was dTC/dq = 10 + 2q. The new MC will be 18 + 2q.
With 200 firms in the industry (in the short run), Q = 200q, or q = Q/200. The new supply curve
for the industry is therefore P = 18 + 2(Q/200) = 18 + 0.01Q. Putting this together with the
industry demand curve (P = 170 - 0.03Q), we find the equilibrium quantity traded in the industry
is 3,800 units and the new equilibrium price with the tax included is $56. At this price, firms
will want to produce where P = MC or 56 = 18 + 2q. Therefore, 2q = 56 - 18 = 38, or q = 19.
The correct answer is (R).
13. Each firm earns profit of TR - TC = P  q - 400 + 18q + q2 = (56  19) - (400 + [18  19] +
[19  19]) = -$39, or a loss of $39. The correct answer is (N).
14. In the long run, in this perfectly competitive constant cost industry, every firm will operate at
the minimum point on its long run average cost curve (including the tax). This minimum cost
will be $50 + $8 = $58. In other words, the long-run supply curve is given by P = $58. Putting
this together with the demand curve (P = 170 - 0.03Q), we find that 0.03Q = $112, or Q =
3,733.33. Since each minimum cost firm will be producing at q = 20, there will be about 187
firms in this industry in the long run. The correct answer is (H).
15. In the short run, the price rose from $50 before the tax to $56 after the tax (see the answer to
question 12). In other words, the buyers= share of the tax in the short run was $6. The correct
answer is (F).
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