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Unformatted text preview: Prof M Bacolod
ECON 100B
Winter 2005 Additional Review Problems: Factor Markets to ISLM 1. Explain whether the following statements are true, false or uncertain. A correct answer without
justiﬁcation will receive no credit. (a) Suppose the market for widget factory workers is competitive and the market for widgets is
competitive. If the widget industry were to be taken over by a monopolist, the monopolist would
hire less labor than was hired when the industry was competitive. (b) The supply of labor bends backward because as the wage rate becomes high enough, the substi—
tution effect and income eﬁ‘ect work in the same direction. (c) Wages and employment levels are indeterminate when the union has monopoly power and the
ﬁrm has monopsony power. (d) Asymmetric information between buyers and sellers lead to market failure even when a market is
otherwise perfectly competitive. (e) Life insurance companies typically require that an applicant for a. life insurance pOIiCy go through
a medical examination. Such a requirement helps prevent the problem of moral hazard. 2. Xtran is a monopolist company for a new patented food supplement for athletes. If the demand for its
product is P = 25 w 26,2, and the ﬁrm’s short—run (i.e., capital is fixed) production function is Q : 4L.
Derive the ﬁrst order condition and the ﬁrm’s demand for labor as a function of market wages. 3. Suppose that a person’s utility can be expressed as U = J? + x/f where I is income, L is leisure hours.
In particular, L = 24 — H (since there are only 24 hours in a day), and I z w a: H where H is the
number of hours worked. (a) Derive this person’s labor supply curve.
(b) At hourly wages in = $5, what is the optimal hours worked by this person? At w : $11? (c) Fill in the following table to indicate an increase (T) or decrease (i) to answer this question.
Using this individual’s response to the wage change, can you tell if the income or substitution effect dominates?
— Effect on leisure (L) Effect on work hours (H)
SE
IE
Total Effect __ 4. A ﬁrm located in Los Angeles makes jackets using a production function given by Q = 10L — 0.5132
where Q is the number of jackets produced per hour and L is the number of workers. Labor is the only
factor of production. The ﬁrm can sell as many jackets as it wants at a price of $4. Suppose the ﬁrm
is a monopsonist in the labor market such that it faces the labor supply curve: W = 2L where W is
the wage. (a) Write down the proﬁts of the ﬁrm in terms of L. (b) Take the ﬁrst order conditions and ﬁnd the optimal level of the wage and employment for the
ﬁrm. (c) Write out the equations of the Marginal Revenue Product (MRP) of labor curve and the marginal
expenditure curve, and carefully draw a picture with the labor supply curve. Show the outcome you found in part (b) on this graph. (d) Suppose the City of Los Angela; imposes a minimum wage of $16 on this market. What is the
eﬁ'ect on wages and employment for the ﬁrm? 5. Suppose consumers are willing to pay as much as $5,000 for a good used car but only $1,000 for a
“lemon.” Sellers of good used cars require at least $4,000 per car and sellers of “lemons” require $800.
Suppose 40% of all used cars are "lemons." Buyers know this, but cannot tell if a used car is a “lemon”
or not. Which of the following will occur? (a) All cars will be sold for $3,400.
(b) Only lemons will be sold for $3,400.
(0) Only lemons will be sold for $1,000.
(d) All cars will be sold for $1,000. 6. Suppose low—productivity workers have a marginal product of 5 and high—productivity workers have a
marginal product of 9. Workers are evenly divided into the two groups. If competitive ﬁrms, whose
product sells for $5,000, cannot identify people’s productivity before they are hired, then (a) Only low—productivity workers will be hired at a wage of $25,000.
(h) Only high—productivity workers will be hired at a wage of $35,000.
(c) Workers of both types will be hired at a wage of $35,000. (d) Workers of both types will be hired at a wage of $25,000. 7. Suppose that obtaining a college education signals to a prospective employer that one is a high
productivity worker. For high—productivity workers, the cost of a college education is $20,000 per year,
and for low—productivity workers, the cost of a college education is $30,000 per year. If a ﬁrm believes
a worker to be a high—productivity worker, it will pay the worker $100,000 more over the worker‘s
lifetime than the ﬁrm would pay a low—productivity worker. What is the number of years of college
education the ﬁrm will assume is a “signal” that a worker is a highproductivity worker? 8. Consider a small exchange economy with only two commodities, quiche (q) and wine (in). There are two
individuals, Ken and Barbie, whose preferences are given by Uk(qk, wk) = qkwk and Ub(qg,, wb) = qbwb,
where (qk, wk) and ((15,, wb) are the allocation of quiche and wine for Ken and Barbie, respectively. Ken has 4 quiches and 3 bottles of_wine, and Barbie has 2 quiches and 6 bottles of wine.
I (a) Draw an Edgeworth box and depict: the initial allocation (6), the set of Individually Rational
allocations (IR), and the set of Pare’to Optimal allocations (PO). (b) Is the allocation that Ken gets 3 quiches and 6 bottles of wine mutually beneﬁcial? Explain. Is it
Pareto efﬁcient? Explain. (c) Verify if the allocation (qk,w;,) = (3, g) and ((155,105) = (3, g) is on the contract curve. Can Ken
and Barbie make trades and still do better? 9. Consider a two—person pure exchange economy with two goods, w and 3;. Consumer 1 has utility function
u1($, y) = x'3y'7 and is endowed with 10 units of a: and 20 units of y. Consumer 2 has utility function
U2(SD, y) = :r'5y'5 and is endowed with 20 units of :r and 5 units of y. (a) Draw a. reasonably accurate Edgeworth box and depict clearly: the initial allocation (6), the set
of Individually Rational allocations (IR), the set of Pareto Optimal allocations (PO), and the core of this economy (C). r , .. _, (b) Is the allocation (ethyl) = (15,175) and (m2,y2) : (15,175) Pareto efﬁcient? W MACRO 10. Illustrateand explain what eﬁ‘ﬁtﬁa Earl 39.19.29, bonds will have on: (1) the goods market; (2) the
Ms J' money market; (3) thlﬁW aid 4) the IS curve
5‘ s 11. Illustrate and explain what effect an Wﬂon: (1) the goods market, (2) the
money market; (3) the LM curve; and (4) the IS curve. 5M3; femw" goUDS 12 Using the IS—LM graph, show what eﬁ'ect an increase in government spending will have on output, the Wm
WM 13. Using the IS—LM graph, show what effect a reduction in money supply will have on out ut, the interest rate, and investment. (90095 14. Use the IS—LM model to answer this question. Suppose there 1s a. simultaneous increase in taxes and MM W13! Explain what effect this particular policy mix wil have on output and
the interest rate. Based on your analysis do we know with certainty what effect this policy mix will have on investment? Econ 100B
Select Answers for Practice Problem Set #1 Jun Ishii * Department of Economics
University of California, Irvine Spring 2006 1 Textbook Exercises (In) Chapter 8, Exercise 5 in (PR)
What level of output will the ﬁrm produce ?
Proﬁt maximization implies that each ﬁrm will behave such that marginal revenue (MR) equals marginal cost (MC). In a competitive market, ﬁrms are pricetakers. Therefore, their marginal
revenue is simply the market price. Bamm PC. 3/ = 3+2q
(ﬁrms mPrLo’mUJ‘S MR MC
pzzma Therefore, q = 3 for the competitive ﬁrm What is the ﬁrm’s producer surplus ? Producer surplus is the area below the market price but above marginal cost. The quantity at
which “P=MC” is 3 (3 + 2 x 3 = 9). Therefore, producer surplus corresponds to the area of a
triangle with a height of 3 units and a base of 6 ($9 — $3}, namely $9. Will the ﬁrm be earning a positive, negative, or zero proﬁt in the short run? Note that this AVC and the earlier marginal cost functions are consistent with each other. Marginal
cost is the derivative of total variable cost with respect to quantity. Total variable cost is average variable cost times quantity: MC = 1%[9 = 8%;(3'1 + (12) = 3 + 2g ’Oﬁice: SSPB 2279 E—mail: jishii©ucLedu TA: Eric Ayzenshtat ([email protected]) Shivraj Singh ([email protected]) Therefore, this price—taking ﬁrm will also make 3 units at the market price of $9. Total cost is simply total variable cost plus ﬁxed cost: $(3 + 3) X 3 + $3 = $21. Total revenue is $9 x 3 2 $27.
Therefore, the ﬁrm makes a proﬁt of $27 — $21 2 $6. (1b) Chapter 10, Exercise 12 in (PR) First, let us calculate the inverse demand 10,000 10,0
Q(P)= P... a P(Q)= 72$ Total revenue and marginal revenue for this monopolist are TR = PxQ = 102:0on = 100g)“5
MR _ 8Q _ 50Q Short run total cost and short run marginal cost are SRTC = 2,000+5Q BSRTC
SRMC — 6Q  5 As shortrun proﬁt maximization implies SRMR = SRMC 50 02—05 = “5/
SRMR SRMC Therefore, the proﬁt maximizing quantity for the monopolist in the short run is 100 units. The proﬁt maximizing proﬁt in the short run is P 100 = 100 = $10. The short—run maximized prof
10,000 its are $10 x 100 —( 2000+5 X 100) = —$1, 500. So the monopolist is losing money in the shortrun. However, keep in mind that the monopolist’s ﬁxed costs are sunk in the short—run. The $2,000 is
irrecoverable, regardless of whether the monopolist decides to produce Q = 0 or Q = 100. There
fore, thc monopolist should keep producing as long as P 2 SRMC, which they are at Q = 100. In the longrun, the total cost is 6 x Q and the marginal cost simply $6 per unit. This implies a long—run proﬁt maximizing quantity of (%)2, price of $12, and proﬁt of $3? We might expect larger marginal costs in the longrun as in the longrun, all inputs must be re—
placed, including inputs that are ﬁxed in the shortrun. (1c) Chapter 10, Exercise 18 in (PR) Note that total cost can be decomposed as follows:
Total Cost = Fixed Cost + AVC x Q So the marginal cost for this problem is simply _ 8 0.5 0.5
MG _ 56? [5+Q xQ] _ 1.5XQ
Marginal revenue can be solved as in the earlier problem. By setting MR=MC, we ﬁnd that the
proﬁt—maximizing price, quantity, and proﬁt are: P = $6, Q = 4, proﬁt 2 $11. Note that the government price ceiling is binding: with no ceiling, the monopolist would want to
charge $6 > $4. Therefore, we need to consider how the marginal revenue changes with the presence of this price ceiling. From the inverse demand function, we knew that the price ceiling is binding at Q S 9. Therefore _ $4 irogg P — % ifQ>9
4 irogg MR = {765g ifQ>9 Note that at Q = 9, MC = 4.5. As MC is strictly increasing with Q and MR strictly decreasing with Q (for Q > 9), we know that MR and MC must intersect at some quantity below Q = 9. Setting MC equal to 4Q, we ﬁnd that the proﬁt maximizing quantity is now 6.74 m 7 units. In order to induce the monopolist to produce as much as possible, we want the ceiling set at the price where the demand function intersects with marginal cost  i.e. the price for a competitive ﬁrm. 7%=1.5xQ“5—»+Q=8—>P=% (1d) Chapter 13, Exercise 6 in (PR) There are 2 pure strategy Nash equilibria:
0 (AC): Firm 1 plays A, Firm 2 plays C
0 (CA): Firm 1 plays C, Firm 2 plays A Both ﬁrms maximin strategy is to play A. So the maximin outcome is (A,A) with a payoff of (10,10) Firms 2’s best response strategy given that ﬁrm 1 is playing A (maximin) is to play 0. #1
ﬂ_ . 2 Solving for Nash Equilibria Game 2
Game 1 Player 2
Player 2 L C R
A T “m
Pla er 1 B Player 1 M1
y G M2
B For Game 1: I No dominant strategies for either player 0 Player 1: B strictly dominates C 0 Player 2: G strictly dominates H 0 Single pure strategy Nash equilibrium: Player 1 plays B, Player 2 plays G
For Game 2: o No dominant strategies for either player .. Player 1: T strictly dominates B 0 Two pure strategy Nash equilibria:
(M1, L): Player 1 plays M1 and Player 2 plays L
(M2, C): Player 1 plays M2 and Player 2 plays C Also, solve for any pure strategy Nash equilibria in each of the three games (Prisoner’s Dilemma,
“Chicken,” Matching Pennies) in the Lecture 1B notes. HINT: One of the games has an unique pure strategy Nash equilibrium, another more than one, and still another none. 0 Prisoner’s Dilemma has an unique pure strategy Nash equilibrium, “Chicken” has two pure
strategy Nash equilibria, matching pennies has no pure strategy Nash equilibrium (but it does have a single mixed strategy Nash equilibrium). For the Matching Pennies Game, show why each player playing the mixed strategy Heads with
probability 0.5 and Tails with probability 0.5 is a (mixed strategy) Nash equilibrium. To do this,
show how each mixed strategy is a best response to the other mixed strategy. Consider other mixed
strategies (i.e. change the probabilities such as heads with 0.75 and tails with 0.25 probability). You’ll ﬁnd that there are no other Nash equilibria. 0 Just show that the best response strategies do not match up for probabilities other than 0.5 0 Keep in mind that players are now maximizing expected payoffs ...
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 Spring '05
 Bacolod

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