FRE UBC
Commerce/ 295
MIDTERM EXAM ANSWERS
October 26, 2009
NAME:__________________________
STUDENT NUMBER ________________
SECTION: _______________________
PROFESSORS NAME: _______________________
Instructions: This exam will be marked out of 100. You will have 1 hr. and 45 minutes to do the
exam. There are two parts to this exam. The first part is true-false questions. Answer all of these
questions. Part II consists of longer questions. You must choose 4 out of 5 of the longer
questions in Part II.
This midterm has 16 pages. Check now to make sure you have all pages and make sure your
name, section, and student number are provided above.
This is a closed-book exam. You may not use books or notes. You may use a non-graphing, nonprogrammable calculator.
GRADES
True/False
Long Answers:
________ / 40
1. ________ / 15 (answer 4 out of 5)
2. ________ / 15
3. ________ / 15
4. ________ / 15
5. ________ / 15
TOTAL ________ / 100
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PART I
TRUE-FALSE QUESTIONS
Mark each question as true or false, by putting an X in the appropriate box.
There is one mark for each true-false question.
1. In a perfectly competitive market for gasoline, determine which of the following
statements are true and which are false.
True False
Assuming the supply of gasoline slopes upward, an increase in the price
of electricity-based public transportation is likely to cause the price of
gasoline to rise.
If the demand for gasoline were linear, technological progress in gasoline
production that shifts the market supply curve to the right is very likely to
lead to higher industry-wide revenues.
If gasoline is a normal good it follows that the supply curve would tend to
shift in (left) during a recession.
Suppose demand is linear and downward sloping and supply is perfectly
elastic (flat). If demand were to make a parallel shift to the right, then
demand would be less elastic at the new equilibrium point than at the old
equilibrium point.
2. The company BC Bread has the production function q=KL, where K represents
equipment and L represents labour (employees). The price of labour is $w and the
rental rate on equipment is $ r.
True False
BC Breads production function has constant returns to scale.
BC Breads production exhibits a diminishing marginal product of labour.
If the firm lays off workers it will increase the average product of labour.
BC Bread has a U-shaped long run average cost curve.
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3. Determine if the following statements about government intervention in a
competitive market are true or false.
True False
If demand is perfectly elastic and the government imposes a per-unit tax,
the price consumers pay will not be affected.
Consumers will tend to bear more of the incidence of a per unit tax (i.e.
pass-through of the tax to consumers will be greater) if the good being
taxed has close substitutes that are untaxed.
Government subsidies can cause over-production relative to the level of
output that maximises total surplus.
An effective price ceiling increases consumer surplus for those who are
able to purchase the good without additional search or waiting costs.
4. Determine whether the following statements about pricing with monopoly power are
true or false.
True False
If a monopoly firm switches from standard monopoly pricing (MR = MC
with a single or uniform price) to perfect price discrimination, the gain
in the monopolist's producer surplus equals the loss in consumer surplus.
If a monopoly firm facing many consumers with different demand
functions can charge different entrance fees to each of them as a part of its
two-part tariff scheme, then it would maximize its profits by charging the
same usage fee P = MC to all of them.
If a monopoly firm faces two groups of consumers with very different
demand functions, then the firm might maximize profits by selling only to
the group with the higher demand.
A monopoly firm that uses quantity discounts would reduce its profit
because, in effect, it offers lower prices than necessary to high volume
customers.
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5. Determine if the following statements about monopoly are true or false.
True False
A monopolist facing a downward sloping linear demand curve
maximizes its profits by producing on the inelastic portion of the demand
curve.
If a monopoly firm has the cost function given by C(Q) = 200 + 4Q, then it
must be a natural monopoly.
If a profit-maximizing monopoly produces where the elasticity of demand
is -1, then marginal cost must be zero at that point.
If a monopolys profit-maximizing price is $3 and the price elasticity of
demand Ed at this level is -3, then the marginal cost of production at that
level of production must also be equal to $3.
6. George is trying to pick a cell phone plan. He is concerned about two attributes: voice
minutes and text messages. George has smooth, standard-shaped, convex downward
sloping indifference curves over these two attributes and will consume positive
amounts of both attributes.
True False
If the price of text messages decreases, George will necessarily be better
off.
If Georges utility from plan A is 10 and from plan B is 20, George would
necessarily be willing to pay twice as much for plan B as for plan A.
The greater the number of text messages George has, the more text
messages he could give up to get an additional voice minute and maintain
the same utility.
Doubling the price of text messages and voice minutes will have no effect
on Georges budget constraint.
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7. Green Acres produces corn in a perfectly competitive industry with an upward
sloping marginal cost of production and positive fixed costs. The corn industry consists
of a large number of farms which have the same cost structure as Green Acres.
True False
In the long run competitive equilibrium, the price of corn is equal to both
the marginal cost of production and the average total cost of production
for Green Acres.
If new farmers start entering the industry because short run industry
profits are positive, then Green Acres will increase its production in order
to maintain its market share.
If the market demand for corn shifts up and to the right, then in the short
run (before entry by new farmers), the average total cost of production for
Green Acres will increase.
Suppose the corn industry is currently in a long run competitive
equilibrium. If all farmers are now required to pay an additional $10 tax
per unit of production, then Green Acres will produce more corn as the
industry adjusts to a new long run competitive equilibrium.
8. Which of the following statements about the organization of the firm are correct?
True False
The separation of ownership and control in large modern corporations
often leads to agency problems.
Corporations that go bankrupt earn insufficient profit and are therefore
part of the non-profit sector.
If managerial compensation is structured as an increasing function of the
firms revenue we might expect the firms output to exceed the profitmaximizing level.
Profit maximization requires MR = MC except under perfect competition
where the rule P = MC applies instead.
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9. Joanne prefers consumption bundle A to consumption bundle B and she prefers
consumption bundle B to consumption bundle C.
True False
By transitivity Joanne must prefer A to C.
By non-satiation (more is preferred to less) Joanne must prefer A to C.
Bundle A must be more expensive than Bundle C.
Bundle A cannot include any pair of goods that are perfect complements.
10. Potter Enterprises produces magic wands and wizards robes. Wands and robes are
produced by magical methods so the cost of production is zero. There are three
potential customers. Their willingness to pay for robes and wands is shown by the
following table. (Each customer would buy at most one robe and one wand.)
Robes
Wands
Consumer A
70
20
Consumer B
50
40
Consumer C
30
90
True False
Potter Enterprises can earn higher profit by selling robes and wands as
bundles rather than by stand-alone monopoly pricing.
Bundling generates higher profit than first degree price discrimination
would in this case.
This example illustrates negatively correlated willingness to pay for robes
and wands by these three customers.
The maximum profit that can be earned under bundling exceeds 250.
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Part II
LONGER ANSWER QUESTIONS
Answer only 4 of these 5 questions. Please show your working and answer the
question within the space provided.
Question 1
Jenny is at a hockey game, trying to decide how many nachos (N) and sodas (S) she
should purchase.
a) Jenny has an available budget of $16, the price of a basket of nachos (PN) is the
price $4, of soda (PS) is $2. On a graph with nachos on the horizontal axis and soda on the
vertical axis draw the budget line. What is the algebraic form of this budget line? (5 pts)
S
10
8
5
4
5
10
N
To derive this budget line we note that PNN + PSS = 16. Rearranging yields S = 16/PS
(PN/PS)N or S = 8 2N.
The budget line can be expressed as 16 = 4N + 2S or 8 = 2N + S or S = 8 2N. Any of
these forms is okay for 2 pts.
b) Jennys marginal utility of a can of soda is 1/S and her marginal utility of a basket of
nachos is 1/N. If she currently has 2 baskets of nachos and 4 sodas, what is her
marginal rate of substitution (MRS). Interpret the MRS in words. (5 pts)
With S on the vertical axis, MRS = -MUN/MRS = -(1/N)/(1/S) = - S/N. With N=2 and
S=4, her MRS is -2, meaning she would be willing to give up two sodas to get an
additional basket of nachos.
c ) Given the prices, Jennys budget, and her preferences, how many sodas and nachos
will she purchase? (5 pts)
Setting MRS=MRT yields: - S/N= - 4/2 =>N=S/2.
Substituting this back into the budget constraint, S = 8 - 2(S/2)
=>S = 4 and N =S/2 = 2 baskets.
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Question 2:
We Make Bikes Inc. (WMB) has the following production function for bicycles:
q=K0.5L0.5, where q stands for the number of bicycles produced in one day, K is the
amount of machine hours and L is the amount of labour hours. Input prices (the rental
rate on machine time and the wage rate) are fixed.
a. Find algebraic expressions for the marginal product of labour (MPL) and for the
average product of labour (APL). Now, assume that WMB hires machines for 4 hours a
day. Does the production function exhibit diminishing marginal returns to labour? (6
pts)
MPL(K,L)=dq/dL=0.5K0.5/L0.5, APL(K,L)=q/L=K0.5/L0.5
MPL(4,L)=dq/dL=0.5(40.5)/L0.5 =1/L0.5, dMPL/dL= - 0.25/L1.5<0. This implies that
the marginal product of labour falls as labour rises, or that the production function
exhibits decreasing marginal returns to labour.
b. Show that the production function exhibits constant returns to scale. (5 pts)
A production function has constant returns to scale if increasing inputs by some
percentage causes output to increase by the same percentage. For example, doubling
inputs would double output. In this case we can substitute 2K and 2L instead of L and
K into the production function to get:
q(2K, 2L)=(2K)0.5(2L)0.5=(2)0.5+0.5(K)0.5(L)0.5=2K0.5L0.5, which equals 2q. Thus doubling the
inputs generates twice as much output, which implies constant returns to scale.
c. Explain what constant returns to scale implies about the relationship between long
run marginal (MC) and long run average cost (AC), given that input prices are fixed. (4
pts)
With constant returns to scale and fixed input prices the AC is flat (or remains
constant), which implies that AC=MC for every quantity produced.
Question 3
Suppose a number of identical firms produce handmade bicycle frames in a perfectly
competitive market. Total long run monthly costs for a typical firm are given by C(q) =
20q2 + 10q + 2000, where q = number of frames produced/month. Market demand for
the frames is given by Q = 2,000 - 3P, where Q = quantity demanded/month and P =
market price.
(a) Derive algebraic expressions for the firms long run average cost and long run
marginal cost. (4 pts)
MC = dC/dq = 40q + 10.
AC = C/q = 20q + 10 + 2000/q.
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(b) In the long run competitive equilibrium price must equal average cost. How many
frames will each firm produce and what price will it charge? (5 pts)
Profit maximization implies that P = MC. Also P = AC in the long run.
It follows that MC = AC.
Therefore, 40q +10 = 20q+10+2000/q
=>
q* = 10.
Long run equilibrium P* = MC(q*) = 40*10+10 = $410
(c) Now suppose that market demand for the handmade frames shifts to the right (due
to their increased popularity), and as a result the existing firms start making profits in
the short run. This short-run profitability attracts new (but identical to existing ones)
firms into the market that are identical to the earlier firms. This puts an upward
pressure on the rents the firms are paying for their offices. Draw a diagram showing
Marginal Cost and Average (Total) Cost Curves for a typical firm. Illustrate how this
increase in fixed cost (due to higher rents) would affect the long-run equilibrium price
and quantity each firm produces. No numerical calculation is necessary. The diagram
does not need to be to scale but show the relationships among the curves. (6 pts)
The increase in FC would shift AC curve upwards (but not MC curve). As a result both
long-run equilibrium price and quantity each firm produces increase.
Question 4
Answer the following questions about monopolies and pricing strategies with market
power.
(a) The demand for a monopolists product is given by QD = 100 2P. The monopolists
cost function is given by C(Q) = 10Q + 0.5Q2. Demonstrate algebraically that the profit
maximizing price, P*, exceeds marginal cost. (5 pts)
Invert the demand schedule to obtain P = 50 - 0.5Q. The marginal revenue schedule is
the same as demand except it has double the slope: MR = 50 Q. Marginal cost is found
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by differentiating the cost function with respect to Q: MC = 10 + Q. Maximizing profits
requires MR = MC 50 Q = 10 + Q. Solve this equation to get Q* = 20. Substitute Q* =
20 into the inverse demand schedule to obtain P* = 50 - 0.5(20) = 40. With Q* = 20 we
have MC* = 50 20 = 30. Therefore, P* > MC.
(b) What is the point elasticity of demand at the profit maximizing price and quantity?
Explain why demand must be elastic at the profit maximum. (5 pts).
E = (dQ/dP)(P/Q) = -2(40)/20 = - 4.
If demand is inelastic the firm can increase revenue and lower cost by raising price and
therefore would increase profit. Thus demand cannot be inelastic at the solution.
Demand cannot have elasticity of -1 because the firm could raise profit by raising price,
keeping revenue constant and lowering costs. Therefore, only if demand is elastic can
the firm be maximizing profit.
(c) Your job as a public regulator is to ensure that a monopoly supplier of electricity to a
large copper smelter earns zero economic profit. You have two options: (A) require the
monopolist to charge the smelter P0 per unit of electricity sold; and (B) require the
monopolist to charge the smelter a fixed access fee T (which is independent of electricity
consumption) plus P1 per unit of electricity sold. Label the left-hand graph below with
P0 to illustrate zero profits for the monopolist. Label the right hand graph below with P1
and T to illustrate zero profits for the monopolist. Explain whether A or B is the most
efficient pricing scheme for society. (5 pts)
Scheme A
Scheme B
Smelter
Demand
ATC
ATC
P0
MC
DWL
Price P0 per unit sold
MC
P1
Area of Rectangle = T
Access fee T plus Price P1 per unit sold
Scheme B results in a more efficient scheme for society because there is no deadweight
loss (DWL). However Scheme A causes DWL as P > MC in this case.
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Question 5
Suppose that Evier and Perrian produce a particular type of mineral water. They are the
only firms with access to the necessary mineral springs so no other firms are in the
market. Output is measured in cases (12 bottles per case) and is homogeneous. The
marginal cost of production is the same for both firms and is constant at $10 per case.
Demand for cases is given by (inverse) demand curve P = 100 Q where Q = QE + QP.
(Subscript E and P stand for Evier and Perrian respectively.)
a) In the context of the Cournot oligopoly model, show that the best-response curve for
Evier is given by QE = 45 QP/2. (5 pts)
For Evier: R = PQE = (100 (QE + QP))QE = 100QE QE2 QEQP.
MR = dR/dQE = 100 2QE QP. MC = 10.
To maximize profit Evier should set MR = MC, yielding 100 2QE QP = 10.
We can rearrange this equation to obtain QE = (100 10)/2 QP/2 or
QE = 45 QP/2. This equation shows the profit maximizing or best output for Evier
for any output level chosen by Perrian.
b) Calculate the Cournot equilibrium quantity and price. (6 pts)
The best response curve for Perrian is derived in the same way and can be written as QP
= 45 QE/2. This can be rewritten as QE = 90 2QP. The two best response curves are
two linear equations in two unknowns that can be solved: QE = 90 2QP = 45 QP/2. It
follows that 3QP/2 = 45 or QP = 30. QE also equals 30 so Q = 60. Price is given by 100 Q
= 40.
c) Provide a diagram showing the best response functions and the Cournot equilibrium
solution. Put QE on the vertical axis and QP on the horizontal axis. The diagram does not
need to be to scale but determine the intercepts. No explanation is necessary. (4 pts)
QE
90
Best Response Curve of
Perrian
Cournot Equilibrium
45
30
Best Response Curve of Evier
QP
30
45
90
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