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Unformatted text preview: ARE 100b Spring 2009
HOMEWORK 3 due Thursday, June 4th, in class 1. A ﬁrm produces circuit boards according to the production function qj = lOLi".
The ﬁrm is a competitive price-taker. a. Write the ﬁrm’s proﬁt ﬁmction in terms of P, Li, w and FCi. b. What is the ﬁrm’s derived demand function for labor? (Answer will be in terms of P and w.)
c. Suppose there are 5 identical competitive ﬁrms that hire labor in this market. What is the
industry demand function for labor? Now suppose the ﬁrms’ circuit boards sell worldwide in a
competitive market, at price P = $50; and local labor supply in the region is LS = 30w. What is
the market equilibrium wage? How many units of labor are hired by each ﬁrm, and by the
industry as a whole? How many circuit boards are produced? d. Based on your answer to 0, ﬁnd the marginal product of labor and the value marginal product
of labor for this industry. Is labor being exploited? Why or why not? e. Now imagine that there is only ﬁrm employing labor in the local area, which acts as a
monopsonist. (Again, assume q,- = 10L;6 , P = $50, and LS = 30w). Find Li, w*, and Q. Is this
ﬁrm exploiting labor? Show why or why not. 2.An industry produces handmade rag dolls. Each doll requires 2 yards of cloth, 3 yards of yarn,
and 1/2 hour of labor to produce. Market information: The supply of cloth is perfectly elastic at pc = $3 per yard;
The supply of yarn is perfectly elastic at py = $.30 per yard;
The supply of labor is Ls = 10 w;
The inverse demand for rag dolls is P = 609.9 - 5 Q a. Write the production function in terms of cloth C, yarn Y, and labor L. What is this functional
form called? b. Suppose there are a number of small competitive ﬁrms that produce these dolls. In long—run
competitive equilibrium, how much of each input will be used by the industry? How many dolls
are produced by the industry? What is the price per doll? What is the market wage? How much
money does the industry spend on each input, and how does this compare to total industry
revenues? c Repeat question b, but assume there is a single doll producer who is a monopolist in the output
market. d. Repeat question b, assuming there is a single doll producer in the area, who ships the dolls into
a competitive global market where P = $9.90, but who is a monopsonist in the local labor market. 3. Michael's Custard has a monopoly in the sale of frozen custard cones in Betterton. The
inverse demand for its cones is P = 5.00 - .001*Q Michael's cones require 1 cone (C), 2 scoops of frozen custard (F), and 3 minutes of labor (L)per
cone. (Fixed factor technology). Cones cost 10 cents, ﬁozen custard costs 40 cents per scoop,
and labor costs 9.00 per hour. Input markets are competitive and supply of all inputs is perfectly elastic. a. Write the ﬁrm’s production function for cones in terms of C, F, and L. Now write the proﬁt ﬁmction in terms of Q. b. How many cones are sold? How much revenue is spent on each input? c. If instead Michael's Custard priced its output competitively, what would it charge per cone?
Now how much revenue would be spent on each type of input? 4. The main employers in Brownsville are several underground coal mines. The total demand by
these ﬁrms for labor is LD = 800 - 100*w where w is the hourly wage and L is the number of hours of labor used per day.
The supply of coal miners' labor in Brownsville is L3 = 100w a. If the labor market is perfectly competitive, what is the equilibrium wage? How many hours
of labor are used? Ifeach worker works an 8-hour shift, how many miners are employed per
b. A labor union is organized among the coal miners in Brown Lung. Its goal is to maximize
economic rents to miners. How much labor is supplied by the union (assuming all miners have joined?) What is the
new wage? How many workers are employed, assuming again an 8-hr. shift?
c. If instead the union attempted to maximize total revenues paid to labor (disregarding
opportunity costs of labor in alternative activities), what quantity of labor would be supplied, and
at what wage? 5. Pigeg Wiggly Market is considering whether to use humans (H) or self-scanners (S) to check
out its customers. Humans cost $25/hour to employ, including beneﬁts. Scanners cost $20/hour
to operate. Humans can ring up 30 customers per hour, while scanners can ring up 22. a. Write the production function in terms of H and S, where q = number of customers rung up.
What is the term used to describe these types of inputs?
b. Suppose the ﬁrm’s goal is to ring up the maximum number of customers per hour, while - keeping the total cost of checking them out to $300/hour. What is the optimal # of humans and
scanners to use, and how many customers can be scanned per hour?
c. Now, suppose due to technological advances, the cost of operating scanners declines to
$15/hr. How does this affect your answer to part b? ...
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- Spring '09