Download Midterm #2

Name___________________________________________________________
Student number _________________________________ Lab LF0__________
Economics 203, F01
Midterm #2 and suggested answers
L. Welling
Time: 50 minutes
November 17, 2006
Value: 45 points
Note: Answer all questions on the test sheet. Do all questions. Show all your work, and clearly
label all diagrams. This quiz has 4 pages.
A. (16 points) Each of the following statements is either true or false. State which, and explain
your choice in the space provided. Your answer should include a definition of any term in
italics. Each is worth 8 points.
a) Consumer surplus is the area under the demand curve above the price. For a perfectly
competitive firm, the (inverse) demand curve is horizontal at the market price. Therefore, a
perfectly competitive industry produces no consumer surplus.
Ans: Definition: consumer surplus measures the difference between the total value a consumer
receives from consuming a good and the total cost of acquiring that good; this is measured
by the area under the consumer’s demand curve (or the market demand curve) above the
price. (2)
The demand curves of a consumer and the market both have negative slopes, so this area
exists. (2)
The demand curve facing a firm reflects the firm’s perception that it can sell all it wants at the
going market price: if it raises its price above the market price, no one will purchase from that
firm since many substitutes are available; alternatively, there is no need for the firm to lower
its price to sell its desired amount. (2)
Since a single firm represents a very small part of the market, its demand curve does not
resemble that of the market as a whole. It is the latter which reflects consumers’ willingness
to pay, and hence the appropriate curve for measuring consumer surplus. (2)
False
b) Consider an exchange economy composed of two individuals, with aggregate endowments
of 10 apples and 15 grapes. If the two individuals have identical preferences, giving the
aggregate endowment of fruit to one individual cannot be Pareto optimal.
Ans: an allocation is pareto optimal if it is not possible to find another feasible allocation which
both strictly prefer, or at least one person prefers while the other is indifferent between the
second and the first. Alternatively: not possible to reallocate goods to make one person
better off without making at least on other person worse off. (3)
If one person has all the fruit, and the other none, then the only feasible way to increase the
utility of the second person is to take some fruit away from the first. This will raise the utility of
the second, but lower the utility of the first – therefore the initial allocation (all fruit to one
person ) must be PO. (4)
So long as people are selfish, and non-satiation holds (1 point for selfish, one bonus point for
non-satiation) , this statement is false.
Economics 203 (F01), 2006; midterm 2
Page 1 of 4
Name___________________________________________________________
Student number _________________________________ Lab LF0__________
B: (29 points) Read all sections of this question before you begin.
Each of 1000 identical firms in the perfectly competitive peanut butter industry has a short-run
marginal cost curve given by SMC (q) = 4 + q , where q is the output of an individual firm.
The (inverse) market demand for peanut butter is
P = 10 −
2Q
, where Q is market output and
1000
P is market price.
a) (5 points) Define and derive the short-run supply curve of an individual firm in this
market.
Ans: definition: SR supply gives quantity firm willing to produce for each value of price (1) given
the quantity of the fixed factor (1). To solve for firm’s supply, two steps:
1. if q is positive, firm produces where p=MC , so P=SMC=4+q implies q=P-4
2. this rule gives q>0 only if P>4, so firm will produce q=0 if P<4.
P − 4 if P ≥ 4
if P<4
Short run supply is therefore: q = { 0
P − 4 if P>4
if P ≤ 4
NB can also be written as q = { 0
; I am not fussy about this here.
- max 4/5 marks if forget portion for which q=0.
b) (2 points) Derive the market supply curve.
Ans: market supply curve is sum over individual firms; with 1000 identical firms, this is
1000( P − 4) if P ≥ 4
if P<4
Q= 1000 q = { 0
1.5 points if forget the range over which Q=0
(
e
c) (6) Define and derive the market equilibrium P , Q
firm
(q ) .
e
) , and the output of each
e
Ans: market equilibrium is a price quantity pair such that:
1. all firms are choosing quantity to maximizing profits, taking market price as given;
2. all consumers are maximizing utility, taking market price as given
(alternative phrasing for (1) and (2): each firm is on own supply curve, and each
consumer is on own demand curve)
3; if P>0, quantity demanded = quantity supplied.
(2 points for definition)
To derive: i) substitute market supply curve for Q in inverse demand, and solve for P:
P = 10 −
2Q
2 × 1000( P − 4)
= 10 −
so P = 6
1000
1000
ii) solve for market quantity from supply: Q=1000(P-4) = 2000
iii) solve for firm quantity: identical firms, so each firm produces same quantity:
q=Q/1000=2; alternatively, sub. Price into firm supply curve to solve
directly for quantity.
(2 points for solution for P and Q, 2 points for firm. Problem will come if they erred in
solving for market supply curve. If get supply curve wrong, penalize them for it in part b), and try
Economics 203 (F01), 2006; midterm 2
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Name___________________________________________________________
Student number _________________________________ Lab LF0__________
and mark this part on the basis of what they derived – as if their answer was correct. Of course, if
their technique was wrong, they lose marks.)
d) (3 points) Illustrate the equilibrium of the market, and a representative firm, on page 3.
Be sure to label your axes, and clearly identify the equilibrium.
Use this page for your diagrams for part B. Be sure to label all relevant points.
Points:
- should have two pictures, since putting firm and market on same graph is difficult
- 2 marks for market, 1 for firm
- deduct half the marks if they don’t clearly label the equilibrium,
- deduct half the marks if they don’t clearly label the axes.
Questions continue on page 4.
e) (5 points) If the market for peanut butter is in long-run equilibrium in c), what must be
the profits of each firm in the industry? Explain your answer.
Ans: in LR equilibrium in perfectly competitive industry, each firm must be making zero
economic profits (1) (that is, just cover all costs, including a normal rate of return on investment
(1) ). Otherwise, since entry and exit are costless(1) , the composition of the industry would
change. In the LR firms have the opportunity to adjust their fixed factors; existing firms can exit,
Economics 203 (F01), 2006; midterm 2
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Name___________________________________________________________
Student number _________________________________ Lab LF0__________
or change size, and new firms can enter the industry (1) . These changes will cause adjustments
in supply, and will continue until all economic profits are eliminated.(1)
As a consequence of public attention to peanut allergies, the demand for peanut butter falls; the
new inverse demand curve is given by
P =7−
2Q
.
1000
f) (8 points) If the manufacture of peanut butter is subject to constant returns to scale,
how will the new long-run equilibrium differ from that in (d)? Why?
Ans: With constant returns to scale, long run average cost is constant, so average total cost does
not depend on a firm’s level of production. With CRS, price will also be independent of the scale
of the industry. Therefore with either demand curve, since firms must be making zero profits,
price must be equal to min’m average total cost =6.
- Since price is the same, the only variable which can respond to the decline in demand is
quantity. in the SR, the decline in aggregate demand will lead to negative profits for each existing
firm.
The new LR equilibrium quantity will satisfy: P= 6 = 7 −
2Q
⇒ Q = 500 .
1000
With constant costs, the firm’s SR supply curve will be independent of the scale of operation, at a
price of 6 each producing firm will want to produce 2 units. Thus the only possible new LR
equilibrium in the market is to have only 250 (=500/2) firms. Therefore it must be the case that in
response to the decline in market demand, which resulted in each existing firm making negative
SR profits, 750 firms left the industry.
(I think this reasoning is correct; if you find an error, let me know. Several students seem to have
solved for the new short-run equilibrium obtaining a new price of 5 – below LR avg cost. If they
stop there, give them 3/8. If they get the new equilibrium price and quantity for the market, but
not the firm, given them 6/8)
Economics 203 (F01), 2006; midterm 2
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