Download Test answers - December 2001

ECONOMICS A02Y - INTRODUCTORY ECONOMICS (A Mathematical Approach)
End of term exam: December 2001 – Answers
1. Substituting X = 3 into the PPF, we can calculate that Y = 0.25(100 – 32) = 22.75.
This tells us that the point (X=3, Y=22.75 is on the PPF, rather than inside it or outside it.
Therefore, this point is attainable and efficient. The correct answer is (A).
2. The formula for the opportunity cost of X for points on the PPF is –dY/dX = 0.5X.
When X = 8, this is equal to 4. The correct answer is (C).
3. The value of output is maximized where the ratio of prices equals the opportunity cost
of X measured in units of Y given up. In other words, Px/Py = -dY/dX or 2/1 = -dY/d/X
= 0.5, this implies 0.5X = 2 or X = 4. The correct answer is (E)
4. When consumers’ income falls, demand for pizza, which is a normal good, will fall as
well. Therefore, the demand curve shifts down (to the left). Equilibrium price and
quantity will fall. The correct answer is (A).
5. Beer is complementary to pizza. Hamburgers are a substitute for pizza. If the price of
beer rises, there is a decrease in demand for its complement – pizza. If the price of
hamburgers rises, there is an increase in demand for its substitute – pizza. As a result in
the pizza market, either quantity and price will both rise or both fall or (if the two shifts
cancel each other out exactly) neither will change. The correct answer is (J).
6. The article will cause a decrease in demand for pizza (shift demand curve to the left).
A decrease in wages paid to workers will cause an increase in the supply of pizza since it
is now cheaper to produce (shift supply curve to the right). Therefore, equilibrium price
will fall, but it is uncertain whether the equilibrium quantity will rise or fall (it depends
on the size of the shift in the supply curve and the size of the shift in the demand curve).
The correct answer is (G).
7. Technological improvements will shift supply to the right. The increase in wages will
shift supply to the left. We cannot tell whether these shifts will exactly cancel one
another out. The correct answer is (K).
8. The individual consumer follows the Optimal Purchase Rule by consuming until the
marginal utility of the last unit consumed is equal to the price. We obtain the consumer’s
demand curve, therefore, by setting P = MU. Demand is P = dU/dX = 40 - 4X. If P =$ 4,
then 4 = 40 – 4X, so X = 9. The correct answer is (Q).
9. Consumer surplus (CS) at X = $4 is the dollar value of the consumer’s utility at X = 9
(more exactly, it is the consumer’s utility at X = 9 minus the consumer’s utility at X = 0)
minus the cost of purchasing the good. In this case U – PX = [40(9) – 2(9)2] – (4 x 9) =
$162. The correct answer is (P).
10. The consumer’s demand is given by P = 40 – 4X. Therefore, at a cost of zero for
each additional movie, the consumer will want to watch 10 movies. At X = 10, CS is
$200 minus the flat fee. This compares to a CS of $162 if the consumer chooses to pay
the price of $4 per unit. So, in order to choose the flat fee arrangement, 200 – (flat fee) =
162, or the maximum amount of the flat fee is $38. The correct answer is (Z).
11. An increase in the minimum wage rate will improve the wages of workers who retain
their jobs but will decrease the quantity of labour demanded by employers. Workers who
lose their jobs will be worse off, while low wage workers who retain their jobs will be
better off. The correct answer is (F).
12. Elasticity of demand is -(1/(dP/dQ) x P/Q) = 1/2 x 80/20 = 2. The correct answer is
(D).
13. At a point on the demand curve where demand is elastic, the percentage change in
quantity will be greater than the percentage change in price. With an increase in quantity,
the price will decrease, and the elasticity of the demand curve tells us that the quantity
will increase by a greater percent than price falls. Since the quantity movement increases
total revenue while the price movement decreases total revenue, we can conclude that
total revenue will rise. The correct answer is (B).
14. Accounting profits = sales – dollar cost of producing goods and services = $7000
(sales) - $4000 (raw materials) - $2000 (wages) = $1000. Economic profits = total
revenue – total opportunity cost = $7000 (sales) - $4000 (raw materials) - $2000 (wages)
- $400 (rent given up) - $600 (job salary given up) = $0. The correct answer is (B).
15. The marginal product of labour is dq/dL = 2/3 x12L-1/3 = 8/L1/3. When L = 27, the
MPL = 8/3. The correct answer is (F).
16. When L = 27, q = 12L2/3 = 108. TC = PK x K + PL x L = (27 x 24) + (16 x 27) = 648
+ 432 = 1080. AC = TC/q = 1080/108 = 10. The correct answer is (R).
17. Marginal cost of one more unit of output in the short run (when only labour is
varying) is given by the cost of hiring one more unit of labour (PL) divided by the
marginal product of an additional unit of labour (MPL). MC = PL/MPL = 16/(8L1/3).
When L = 27, MC = (16 x 3)/8 = $6. The correct answer is (N).
18. To find AVC, we subtract fixed cost (FC) from the TC function and divide by q.
AVC = 363/q + 4 + 3q and dAVC/dq = 3 – 363q-2. We can set this derivative = 0 to find
the output level at which AVC reaches its minimum. So, 3 – 363q-2 = 0, or q = 11. The
correct answer is (I).
19. To find AC, we divide the TC by q. AC = 588/q +4 + 3q. dAC/dq= 3 – 588q-2.
We can set this derivative = 0 to find the output level at which AC reaches its minimum.
So, 3 – 588q-2 = 0, or q = 14. The correct answer is (L).
20. Marginal cost is greater than average cost. Since the additions to cost are greater
than the current average cost, the average cost curve must be rising. The correct answer
is (A).
21. To find out how much the firm will produce in the short run, we set P = MC. MC is
the derivative of TC. So, dTC/dq = 3q + 4. Setting P = MC we get $31 = 3q + 4 or q = 9.
The correct answer is (J).
22. At a price of $31, we calculated that the firm will produce 9 units. Therefore, it earns
revenue of 31 x 9 = $279. Total costs can be found with the total cost function as 1.5(9)2
+ 4(9) + 54 = $211.5. The firm therefore makes a profit of $67.50. The correct answer
is (B).
23. The “shut-down price” is defined as the price below which a firm will decide to cease
operating in the short run; in other words, the price below which the firm no longer
completely covers its average variable costs. To find AVC, we subtract fixed cost (FC)
from the TC function and divide by q. AVC = 1.5q +4 + 24/q and dAVC/dq = 1.5 – 24q2
. We can set this derivative = 0 to find the output level at which AVC reaches its
minimum. So, 1.5 – 24q-2 = 0, or q = 4. Substituting this value into the AVC function
gives us 1.5(4) +4 +24/4 = $16. The correct answer is (I).
24. If there are 200 firms, Q = 200q or q = 0.005Q. Firms will set P = MC in the short
run so for each firm P = 3q + 4. Substituting in for Q, we get P = 3(0.005Q) +4 = 0.015Q
+ 4, which is the industry short run supply function for 200 identical firms. Setting
supply = demand we get 0.015Q + 4 = 44 – 0.01Q, or Q* = 1600. Substituting this into
the demand curve we get P = $28. The correct answer is (L).
25. The long-run equilibrium price is the price equal to the minimum point on the longrun average cost (AC) curve. We are told in the question that the minimum point on the
AC curve occurs when P = $22 and q = 6. Therefore, we have 22 = 44 – 0.01Q, or Q* =
2200. The correct answer is (O).
26. If we are in the long run, we know that we are producing at the minimum point on the
AC curve. We also know that at this point, economic profits must be equal to 0. You can
also check this by substituting q = 6 into the TR – TC function. Doing so, you will see
that TR = 6 x 22 = $132 and TC = 1.5(6)2 + 4(6) + 54 = $132. Therefore TR – TC = 0.
The correct answer is (A).
27. Since each firm is producing 6 units and the industry output is 2200, there are 2200/6,
or 366.66667 firms in the industry. The correct answer is (J).
28. The tax will add 5q to the TC function. Therefore, TC = 1.5q2 + 9q + 54 and MC =
3q + 9. The supply curve for the industry is P = 3(0.005Q) + 9 = 0.015Q + 9. Setting
supply = demand we get 0.015Q + 9 = 44 – 0.01Q, or Q* = 1400. Substituting this into
the demand curve we get P = 44 – 0.01(1400) = $30. Since price rises by $2, consumers
bear 2/5 or 0.40 of the tax. The correct answer is (J).
29. We know that the long run price is equal to $22 (LR supply curve). A $5 tax will
shift the supply curve up by $5. Therefore, equilibrium price rises to $27 and consumers
(buyers) bear the full amount of the tax. The correct answer is (Y).
30. Demand is P = 29 - q. Marginal revenue is MR = 29 – 2q. Marginal cost is
MC = 3q + 4. The monopolist will produce where MR = MC, therefore, 29 – 2q = 3q +
4, or q* = 5. The correct answer is (F).
31. Substituting q = 5 into the demand curve, the equilibrium price will be P* = 29 - 5 =
$24. The correct answer is (Q).
32. Demand is P = 24 - q. Marginal revenue is MR = 24 – 2q. Marginal cost is
MC = 3q + 4. The monopolist will produce where MR = MC, therefore, 24 – 2q = 3q +
4, or q* = 4. Substituting q = 4 into the demand curve, the equilibrium price will be P* =
24 - 4 = $20. The correct answer is (M).
33. Demand is P = 52 - Q. Marginal revenue is MR = 52 - 2Q. Marginal cost is
MC = 0. In order to maximize profits, the firm will set MR = MC = 52 - 2Q = 0, or Q* =
26. Substituting into the demand curve, the equilibrium price will be P* = 52 - 26 = $26.
The correct answer is (K).
34. Zero profit implies that price is equal to Average Cost. Because there are only fixed
costs of $480 and no variable costs, the Total Cost function is TC = 480 and the Average
Cost function is AC = 480/Q. At P = AC, we will have 52 - Q = 480/Q, or 52 - Q –
480/Q = 0. Multiply through by Q and rearrange terms to get Q² - 52Q + 480 = 0. We
can solve this using the quadratic formula, to find two possible values of Q, which are Q
= 40 and Q = 12. Only the larger quantity makes sense as a form of regulation of
monopoly. At this quantity, the relevant price will be P = 52 - 40 = $12. The correct
answer is (D).
35. The Gain to Society is composed of Consumer Surplus + Profit. In the unregulated
monopoly position, the consumer surplus will be (52 – 26) x 26/2 = $338. The profit is
TR – TC = (26 x 26) – 480 = $196. The total gain to society is $534. Under the
regulated monopoly, the consumer surplus will be (52 – 12) x 40/2 = $800. There is no
profit when price = average cost, so total gain to society is $800. Therefore the extra gain
to society due to regulation is $266. The correct answer is (J).
36. When a firm is regulated so as to charge price = average cost, the firm has little
incentive to keep its average costs low. The correct answer is (D).
37. The most efficient allocation of resources, the one where Gain to Society will be
maximized, will occur when P = MC, which is where P = $0. The correct answer is
(A).
38. Let “W” stand for the number of units of wheat and “C” stand for the number of units
of corn. In Canada, the production of 1 unit of wheat requires 1 unit of labour and the
production of 1 unit of corn requires 4 units of labour, so we can represent Canada’s
production possibilities by W + 4C = 30, or W = 30 – 4C. In the United States, the
production of 1 unit of wheat requires 3 units of labour and the production of 1 unit of
corn requires 6 units of labour. We can represent U.S. production possibilities by 3W +
6C = 60, or W = 20 - 2C. Then the opportunity cost of corn in Canada is -dW/dC = 4,
while the opportunity cost of wheat is the inverse of this, which is 1/4. The opportunity
cost of corn in the U.S. is -dW/dC = 2, while the opportunity cost of wheat is the inverse
of this, which is 1/2. Canada therefore has the opportunity cost advantage, or
comparative advantage, in wheat, while the U.S. has the comparative advantage in corn.
Since Canada uses fewer resources (units of labour) than the U.S. to produce either wheat
or corn, Canada has the absolute advantage in both wheat and corn. The correct answer
is (A).
39. Since Canada has a comparative advantage in wheat, it will produce and export wheat
while importing corn from the U.S. The correct answer is (A).
40. In the absence of trade, we are told that Canada produces and consumes 14 units of
wheat while the U.S. produces and consumes 12 units of wheat. Therefore, world
production of wheat is 26 units. If trade occurs, Canada will specialize in the production
of wheat (because of its comparative advantage in wheat) and will produce 30 units of
wheat (Canada needs 1 unit of labour for 1 unit of wheat and has 30 units of labour in
total). Therefore, world production of wheat rises by 4 units. The correct answer is
(G).
1. See question on exam. Be sure to draw in marginal revenue. Onthe diagram,
clearly indicate equilibrium price and quantity under monopoly (write in the
numbers associated with quantity and price on the appropriate axis, and indicate
that these values apply to the monopoly case), and clearly indicate equilibrium
price and quantity under competition (write in the numbers associated with
quantity and price on the appropriate axis, and indicate that these values apply to
the perfect competition case). On the diagram, indicate the area corresponding to
consumer surplus under monopoly, consumer surplus under competition, profits
under monopoly, and the deadweight loss associated with monopolization. Fill in
the magnitudes for theses items under the diagram.
Price
130
= CS (competition)
Consumer Surplus
(monopoly)
=CS (monopoly)
=Monopoly Profit
Monopoly Profit
=Deadweight Loss
PM* = 70
Consumer Surplus
(competition –
shown outlined in
bold)
PC*= 10
QM* =120
Qc*= 240
260
Quantity
MR
A monopolist will maximize profit by setting MR=MC. At this point, we have (QM*PM*). Under
competition, price will be set to the point where P=MC. At this point, we have (Qc*,Pc*).
Consumer surplus from competition is $14,400 and consumer surplus for monopoly is $3600. Profits
earned by the monopolist are $7200 and the deadweight loss due to monopoly is $3600.
1b) Notwithstanding the deadweight loss in part 1a, the dynamic benefit of monopoly, as
explained by some economists is:
Monopolists, they claim, is more innovative than competitive firms, spurred on by the
lure of additional monopoly profits
2. See question on exam. On the diagram, indicate equilibrium output as Q*, and
equilibrium price as P*. Shade in the area representing profits.
P
MC
P*
SAC
SAVC
D
Q
Q*
MR
A monopolist will maximize profit by setting MR=MC. At this point, we have (QM*PM*). The
shaded area represents the profits earned by the monopolist.
3. See question on exam. On the diagram, draw in the new demand curve. Clearly
indicate the new short run equilibrium as point 1 and the new long run equilibrium as
point 2, and show the shifts of any curves using arrows. Indicate clearly which shifts
occur in the short run and which occur in the long run. Indicate the mechanism that
moves the economy from short run to long run equilibrium. In one sentence at the
bottom of the page, explain that mechanism.
P
SSR
short – run
SSR1 (increased
supply as new
firms enter)
(1)
(2)
long run
PLR
SLR
D
D1
Q
One sentence description of mechanism:
Short run profits at point (1) lead to the entry of new firms in the long run, moving us to point (2),
returning the price to PLR and profits to 0.