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ECONOMICS A02Y - INTRODUCTORY ECONOMICS (A Mathematical
Approach)
End of term exam: December 15, 2000 – Answers
MULTIPLE CHOICE ANSWERS
1. The increase in popularity for cable television shifts the demand curve for cable TV to
the right (increases demand). The increase in the cost of providing cable TV services
decreases the supply of this service, shifting the supply curve to the left. As a result,
equilibrium price increases, 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 (E).
2. The decrease in consumer incomes will cause a decrease in demand (shift demand
curve to the left). At the same time, an increase in the price of these services will cause
producers of cable TV to reduce the supply of cable TV (and increase the supply of
internet services since they are a substitute in production for cable TV). As a result, there
will be a fall in equilibrium quantity but it is uncertain whether the equilibrium price 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 (H).
3. – The sattelite dish is a substitute (in consumption) for cable TV. Video tapes are a
complement (in consumption) for cable TV. A rise in the price of a substitute will
increase the demand for cable TV; also, a fall in the price of a complement will increase
the demand for cable TV. Demand for cable TV shifts outwards (to the right) and
therefore equilibrium quantity and price of cable TV will rise. The correct answer is
(D).
4. If a demand curve is inelastic, that means that the percentage change in price will be
greater than the percentage change in quantity. When the price is lowered, the quantity
demanded will increase, and the elasticity of the demand curve tells us that the price will
fall by a greater percent than quantity rises. Since the price movement reduces total
expenditures while the quantity movement increases total expenditures, we can conclude
that total expenditures will fall. The correct answer is (A).
5. Substituting X = 7 into the PPF, we can calculate that Y = 512 – 343 = 169. This tells
us that the point (X=7, Y=169) is on the PPF, rather than inside it or outside it. The
formula for the opportunity cost of X for points on the PPF is –dY/dX = 3X2. When X =
7, this is equal to 147. We are instead, interested in the opportunity cost of Y, which is
just the inverse of the opportunity cost of X, or 1/147. The correct answer is (Q).
6. We need to know the elasticity of supply to answer this question. For this, we first
need to calculate the current equilibrium price and quantity. 100 - .02Q = 60 + .06Q, so
.08Q = 40 or Q* = 500. Substituting into the demand function, we find that P* = 100 –
10 = 90. Elasticity of supply at this equilibrium point is 1/(dP/dQ)  P/Q = 1/.06 
90/500 = 3. Since the elasticity of supply can be interpreted as %Q/%P, this means that
in the vicinity of this point on the supply curve, the percentage change in quantity
supplied will be about 3 times more than the percentage change in price (i.e., 3%). The
correct answer is (H).
7. There are a couple of ways to do this question. One is to calculate the new equilibrium
price and the new price received by the sellers and calculate the buyers’ share and the
sellers’ share of the tax. If the demand curve net of the tax is shifted down to P = 82 –
0.02Q, then the new equilibrium quantity will be at 82 – 0.02Q = 60 + 0.06Q, so 0.08Q =
22 or Q1* = 275. The new equilibrium price can be found by substituting into the
original demand curve, so P1* = 100 – 0.02(275) = $94.50. The new price received by
sellers can be found by substituting into the new, net of tax, demand curve, so PS = 82 –
0.02(275) = $76.50. Therefore the buyers bear $94.50 - $90.00 = $4.50 of the tax while
sellers bear $90.00 - $76.50 = $13.50 of the tax. (An alternative way to do the question is
to recognize that BS/SS = ES/ED. The elasticity of demand is given by -(1/.02 x 90/500)
= 9. The elasticity of supply calculated in the previous question is 3. Therefore BS/SS
must be equal to 3/9 = 1/3, which means that if we divide the tax into 4 equal parts, then
the buyers’ share is one part and the sellers’ share is three parts. 18/4 = 4.50, so BS/SS =
4.50/13/50). The correct answer is (J).
8. Total tax revenue is $18 * 275 = $4950. The correct answer is (T).
9. The excess burden of the tax is [(500-275) * 18]/2 = $2025. The correct answer is
(H).
10. Let “W” stand for the number of units of wheat and “C” stand for the number of units
of cloth. In Canada, each unit of wheat requires ½ of a worker and each unit of cloth
requires ¼ of a worker, so we can represent Canada’s production possibilities by 1/2/W +
1/4C = 200, or W = 400 – 1/2C. In Mexico, each unit of wheat requires 2 workers and
each unit of cloth requires 2 workers. We can represent Mexico’s production possibilities
by 2W + 2C = 500, or W = 250 - 1C. Then the opportunity cost of cloth in Canada is
-dW/dC = 1/2, while the opportunity cost of wheat is the inverse of this, which is 2. The
opportunity cost of cloth in Mexico is dW/dC = 1, while the opportunity cost of wheat is
the inverse of this, which is 1. Canada therefore has the opportunity cost advantage, or
comparative advantage, in cloth, while Mexico has the comparative advantage in wheat.
Since Canada uses fewer resources (units of labour) than Mexico to produce either wheat
or cloth, Canada has the absolute advantage in both wheat and cloth. The correct
answer is (I).
11. The payoffs to Sam depend on Sue’s strategy. If Sue uses the natural remedy, Sam is
better off using DDT (payoff of 350). If Sue uses DDT, Sam is better off also using DDT
(payoff of 200). Sam has a dominant strategy of using DDT. You can analyze Sue’s
incentives in a similar way and find that she also has a dominant strategy of using DDT.
Therefore the Nash equilibrium is that both will use DDT. The correct answer is (B).
12. When an industry produces negative externalities (negative external effects), the
social cost of production is higher than the private marginal cost. Private firms
concentrate on the private costs and so do not allocate resources in a socially efficient
way. As a result, a private market, if left to its own devices, will supply too much (not
too little) output. This oversupply could, potentially, be corrected by carefully designed
taxes. Therefore the correct answer is (B).
13. Since P > MR, this must be a monopoly firm, rather than a perfectly competitive one.
Since MR = MC, it must currently be at the profit-maximizing output. We know that a
profit-maximizing monopolist will only produce in the elastic section of the demand
curve (or, if MC = 0, where demand is unit elastic). In this case, MC > 0, so demand
must be elastic. The correct answer is (D).
14. Marginal cost is less than average cost and less than average variable cost. Since the
additions to cost are less than the current averages, both average cost and average
variable cost must still be falling. The correct answer is (B).
15. Demand is P = 92 - .05Q. Marginal revenue is MR = 92 - .1Q. Marginal cost is
MC = 4. The unregulated monopolist will set 92 - .1Q = 4, or Q* = 880. Substituting
into the demand curve, the equilibrium price will be P* = 92 - .05(880) = $48. The
correct answer is (Q).
16. Zero profit implies that price is equal to Average Cost. The Total Cost function is TC
= 6720 +4Q and the Average Cost function is AC = 6720/Q + 4. At P = AC, we will
have 92 - .05Q = 6720/Q + 4, or 88 - .05Q – 6720/Q = 0. Multiply through by Q and
rearrange terms to get - .05Q² + 88Q – 6720 = 0. We can solve this using the quadratic
formula, to find two possible values of Q, which are Q = 1680 and Q = 80. Only the
larger quantity makes sense as a form of regulation of monopoly. At this quantity, the
relevant price will be P = 92 - .05(1680) = $8. The correct answer is (I).
17. The Gain to Society is composed of Consumer Surplus + Profit. In the unregulated
monopoly position, the consumer surplus will be (92 – 48) * 880/2 = $19,360. The profit
is TR – TC = (48 * 880) – 6720 + (4 * 880) = $32,000. The total gain to society is
$51,360. Under the regulated monopoly, the consumer surplus will be (92 – 8) * 1680/2
= $70,560. There is no profit when price = average cost, so total gain to society is $70,
560. Therefore the extra gain to society due to regulation is $19,200. The correct
answer is (D).
18.An increase in fixed costs will not change the marginal cost curve of the firm, and
therefore will not affect the sum of the marginal cost curves which makes up the short run
supply curve in the industry. Therefore, the industry’s price will stay the same, and each
firm will profit-maximize at the same output (where P = MC). However, the rise in fixed
costs will push up average cost, so the profit made by the firm will fall. The correct
answer is (G).
19. The shutdown price is the one at which the firm’s average variable costs and revenues
are equal, in other words, where price is equal to the minimum average variable cost.
AVC = q2 – 8q + 20 and dAVC/dq = 2q – 8. We can set this derivative= 0 to find the
output level at which AVC reaches its minimum. So, 2q – 8 =0, or q=4. Substituting this
value into the AVC function gives us (4)2 – 8(4) + 20 = $4. The correct answer is (C).
20. In a perfectly competitive constant cost industry, the long-run industry supply curve
is horizontal (perfectly elastic). If a flat-rate excise tax of $1 per unit is levied on the
output of this industry the buyers will bear the entire burden of the tax in the long run.
As a result, the price will rise by $1 and therefore consumers will want to consume less,
so industry output will fall. However, each firm will still profit maximize at the same
most efficient output (the minimum point on the long-run average cost curve, which is
shifted vertically by $1). Since price has risen by the same amount as average costs, all
firms still earn zero profit in the new long-run equilibrium. The correct answer is (E).
21. If the firm is in short-run and long-run equilibrium, that means it is earning zero profit
and is producing an output which puts it at the minimum point on its long-run average
cost curve (which must also be the minimum of its short-run average cost curve). This
firm has total costs given by TC = 0.2q2 + 4q + 320. Therefore, AC = 0.2q + 4 + 320/q.
To find the minimum point, take dAC/dq = 0.2 – 320q-2 = 0 or q2 = 1600 or q = 40. At
this output, average cost is AC = 8 + 4 + 8 = $20. The correct answer is (F).
22. At this price, we need to find out how much the firm will be producing. To do so, we
set P = MC. MC is the derivative of TC. TC = 0.2q2 + 4q + 320. dTC/dq = 0.4q + 4.
Setting P = MC we get $14 = 0.4q + 4 or q = 25. The firm therefore earns revenue of $14
* 25 = $350. Total costs can be found with the total cost function as 4(25) + 0.2(25)2 +
320 = $545. The firm therefore makes a loss of -$195. The correct answer is (B).
23. The Optimal Hiring Rule says that a firm should hire workers until the revenue
generated by the marginal worker just equals the cost of hiring that worker, or more
exactly, that MPL * PX = PL. Since the marginal product of labour is dQ/dL = 220 – 2.5L,
we can calculate (220 – 2.5L)2 = PL or (220 – 2.5(46))2 = $210.
The correct answer is (E).
PART II -- TRUE-FALSE/EXPLAIN (10 marks each)
Indicate whether the statements on this page are true or false (or uncertain) and explain
briefly (but clearly) why you believe they are true, false or uncertain. Most of the marks
are given for your explanation. You may use diagrams, words and/or algebra in your
answers. Answer the questions in the space provided below the statements.
24. Output may rise or fall in the short run in a perfectly competitive industry, but there
are always the same number of firms in the industry in the short run.
TRUE. The short run supply curve represents the immediate response of firms to any
shock which might occur (demand shock or supply shock), that is to say, the response of
those firms which are already in the industry. In the short run, the number of firms is
assumed to be constant, and, in addition, the amount of one factor of production (usually
the amount of capital equipment) is assumed to be fixed in amount. Therefore, the short
run supply curve of the perfectly competitive industry has the same number of firms at
any point along it (i.e., at any output). The long run supply curve is different. In fact,
there are a different number of firms at every point along the long-run supply curve. The
major factor which is changing in the long run is the number of firms in the industry. In a
perfectly competitive industry, there is freedom of entry and exit in the long-run. (The
only exception to the rule that there are the same number of firms in the short-run, is if
price should fall low enough that it is insufficient to cover average variable costs. In this
case, firms will shut down in the short run, because it will be more profitable to produce
nothing at all than to produce a positive output.
25. Society would be better off if public goods were produced in perfectly competitive
markets, instead of being provided by governments.
FALSE. It is not possible for public goods to be produced and sold in perfectly
competitive markets, essentially because of the “free rider” problem. Public goods are
characterized by non-rivalry and non-excludability. Non-rivalry in consumption means
that the goods are consumed collectively rather than individually, in other words,
consumers are not rival users of a public good but can use it together (one person’s use of
the good does not reduce the possibility that another person also uses the good). Nonexcludability means that it is not feasible to exclude someone from consuming the good
once it is already produced. Non-excludability means that it is impossible to sell the
good in a standard perfectly competitive market, because once the first person purchases
the good, any other individual will be able to consume this same good. In other words,
any additional purchaser can “free ride” on the purchases of the first person. In general
public goods are provided by the government and are financed not by purchases on the
market, but by compulsory taxation of citizens.
PART III - SHORT ANSWER ESSAYS AND PROBLEMS ( total of 34 marks)
(12 marks)
26. The diagrams below show an initial short and long run equilibrium in a perfectly
competitive firm and perfectly competitive industry. Assume that demand in this
industry falls.
(a) Show the fall in demand on the industry diagram and the firm diagram, show
the change in equilibrium quantity and price in both the firm and the industry
in the new short run equilibrium. (6 marks)
(b) Show the profit rectangle in the short run. (2 marks)
(c) Also, assuming that this is a constant cost industry, show the long run
equilibrium quantity and the long run equilibrium price. (4 marks)
Make sure you label any new curves you draw on the diagrams and also label all
equilibrium quantities and prices using the notation that we have used in class
during the term.
P
MC
AC
P
SSR
Loss
P0*
P1
D
*
SLR
P0*
P1*
AVC
D
qLR=
q1* q0*
Firm
q
D
1
QLR
Q1* Q0*
Industry
A fall in demand will shift the demand curve down (left). Therefore, output in the firm and industry will
drop in the short-run and losses are made (P1*,q1*) (P1*,Q1*). At this price, firms are covering their
AVC, so they will continue to operate.
In the long-run, output in the firm returns to output at minimum AC, but output in the industry falls
further as firms exit the industry.
Q
(12 marks)
27. The diagram below shows a natural monopoly industry.
(a) Label the different curves on the graph. (2 marks)
(b) Show the amount that would be produced in this industry if it were left to
profit-maximize without government interference.(1 mark)
(c) Show the equilibrium price charged.(1 mark)
(d) Show the amount of Gain to Society on this diagram under natural monopoly.
(show this Gain to Society by outlining the area in dark pen, pencil or
marker – do not shade in the area)(3 marks)
Now, imagine that the government decides to regulate this natural monopoly so
that it earns zero profit.
(e) Show the new quantity traded under this regulatory scheme, and the new
price.(2 marks)
(f) Show on the diagram the new amount of Gain to Society (show this amount of
Gain to Society by shading the area in a cross-hatched pattern). Make sure
you label all curves and label all quantities and prices on the diagram. (3
marks)
P
GTS (profit maximization)
GTS (zero profit)
PM*
PAC
AC
MC
D
Q
0
QM
*
QAC
MR
A monopolist will maximize profit by setting MR=MC. At this point, we have (QM*PM*). The
gain to society is shown in bold. With government regulation resulting in zero profit, the
monopolist will produce where AC=D. At this price, the gain to society is the area below the
demand curve and above PAC.
(10 marks)
28. There are only two countries in the world – Canada and Mexico -- and there are
only two goods produced in the world -- food and shelter -- and there is only one
resource available – labour -- with which to produce these two goods. Canada
needs one unit of labour to produce one unit of food and five units of labour to
produce one unit of shelter. In total, Canada has 50 units of labour available.
Mexico needs two units of labour to produce one unit of food and sixteen units of
labour to produce one unit of shelter. Mexico has 80 units of labour available.
(a) Draw the Production Possibilities Frontiers of Canada and Mexico on the
graph below being careful to show the numerical amounts of food and shelter
at each end of the PPF curves. Label the axes on the graph and any curves
you draw. (6 marks)
(b) Assume that each of these countries specializes completely in production of
the good in which they have the comparative advantage. Assume further that
after trade is established between Canada and Mexico, six units of shelter
trades for one unit of food (this is the new international trading ratio, or
international price of shelter). Draw the Consumption Possibilities Frontiers
of both Canada and Mexico on the graph. (4 marks)
Food
60
Canada’s CPF
50
Canada’s PPF
40
Mexico’s CPF
Mexico’s PPF
Shelter
5
6 2/3
10