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Rice
Due December 1
BE 500
Fall 2003
Homework #4: Monopoly, Movies, and Healthies
I. Consider the two firms of Homework #3, question III. Now, suppose these two firms merged to
form a monopoly. The merged firm would be operated with two plants and a fixed cost of 9 in
each plant (thus total fixed costs would be 18). Under this merged monopoly scenario,
A) Describe the new short run industry Q, P, and profit.
B) Determine the new Consumer Surplus, Producer Surplus, and Total Surplus.
C) Compare your answers to A and B with those of Homework #3, question III and determine
the Deadweight Welfare Loss from Monopoly.
II. Consider a small movie house facing buyers from two distinct groups-- old people and young
people. The demand curves of the separate groups for each movie showing are
P = 20 - 6qold
P = 50 - 3qyoung.
The marginal cost curve for the movie house for each showing is
MC(Q) = Q,
(TC(Q) = Q2/2 + FC),
where Q is the total quantity of people attending a performance-- i.e.
Q = qold + qyoung.
Assume that the theater can sell fractional quantities of tickets. (Fractional quantities are allowed,
perhaps because the q's and Q represent more the "average" quantity sold than a fixed number for
each performance.)
A) If the firm could not price discriminate between old and young, what would its price and
sales in each market be? (Hint: Compute the full market demand curve and its marginal
revenue curve without discrimination.)
B) Now suppose the firm can issue discount coupons to either young people or senior citizens.
Which group would get the discount coupons? What would the price be for those who do
not get a discount coupon? How much of a discount would be given to those with a
coupon? What quantity would be sold in each market? (Hint: Compute the sum of the two
individual marginal revenue curves.)
C) If the coupons were costly to produce and circulate, how much would this cost have to be
before the firm scrapped the coupon plan?
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III. You run a convenience store near the University District facing a demand curve for Healthies,
its unique vegetable drinking product,
q = 125 - 25p,
where q is the quantity of Healthies sold per week, and p is the price of Healthies in dollars. The
inputs to Healthy production are a Healthymaker, equipment specialized to Healthy production and
useful for nothing else, juice, and labor. The Healthymaker rents for $20 per week as part of a long
term contract with an equipment supplier and can produce up to 500 Healthies per week. The juice
and labor used for producing Healthies have an average cost of $1 per Healthy at all levels of sales.
A) What is the short run total cost curve for Healthies (per week)?
B) What is the short run marginal cost curve for Healthies?
C) What price would you charge for Healthies to maximize profit?
D) How would your optimal price change, if at all, when each of the following changes
occurred individually:
D1. Rental rates for Healthymakers increased to $30 per week on all newly negotiated
contracts.
D2. Average juice/labor cost rose to $2 at all output levels.
D3. The demand curve for Healthies shifted out to
q = 150 - 30p.
D4. The demand curve for Healthies shifted out to
q = 150 - 25p.
E) A fellow student has argued that D3 and D4 are easy questions, which should involve no
change in price. "Price should not change in response to demand changes, since whatever
quantity you sell will provide enough revenue to cover cost. The only thing that should
change your price is shifts in costs, which should entirely be passed on to consumers."
Critically evaluate the above advice.