# ARE 100B HOMEWORK 1 (part a) Summer 2014

**KnowledgeCats**

1. (20 pts.) Suppose that demand for a particular style of handmade Rwandan baskets is Qd = 1700 - 10P. Each basket maker has the following cost function: TCi = 1000 + 50 qi + .1 qi^2. Given this information, find the market outcomes under the various market structures below.

a. (4) Perfect competition, short-run. Assume that at present, there are 8 basket makers, each operating as a separate, competitive firm.

Solve for market price, quantity per firm, market quantity, and profit or loss per firm. Also find marginal cost and average total cost for each firm. Is this market in long-run equilibrium? How can you tell? What do you expect to happen over the longer run?

b. (4) Perfect competition, long-run. Given the same cost functions above, find the long-run equilibrium quantity per firm, the LR market price, market quantity and equilibrium number of firms. What is the profit or loss per firm? What is MCi and ATCi?

c.(4) Multiplant monopoly. Suppose that a local entrepreneur decides to form a single monopoly by acquiring all the firms from part b and operating them as a single company (Each basket maker will still produce using the same cost function, but all the output will be marketed centrally). Now, how much output is produced at each plant (that is, by each basket maker), and how much by the firm as a whole? What is the monopoly price? What is the monopolist’s profit or loss per plant? What is the firm’s overall profit or loss for all 10 plants together? What is MCi and ATCi? What is MR?

d. (4) Graph the market supply and demand functions from part b (long-run perfect competition.) ( Hint: recall that the market supply function is N*qis). Label Pc and Qc. Then find consumer surpus (CS), producer surplus (PS) and total social welfare (TSW) under this market structure.

e. (4) Now, graph market demand, and the monopolist's industry marginal cost and marginal revenue functions, for the situation in part c. (graph the monopolized market ) Show Pm, Qm and MR=MC. Then solve for CS, PS, and TSW. How much did consumer surplus change due to monopoly? How much did producer surplus change? What was the deadweight loss of monopoly?

2. (10 pts.) In a Napa Valley town, daily demand for wine is Qd = 27000 P^{-3}

a. (2) Prove that the formula above implies a constant elasticity of demand of e_{p} = -3.

b. (5) Suppose the wine industry is competitive, and each firm’s total cost of production is

TCi = 10 qi. What type of market supply function does this give rise to? Find the market price and quantity. If there are 9 identical firms supplying this market, how much does wine does each sell daily, and what is each firm’s daily profit or loss?

c. (3) Now suppose the market for wine is supplied by a single monopolistic firm, having the same cost function as in part b. Find the new market quantity, price and the monopolist’s profit or loss.

3. (5 pts). Boron Industries is a monopolist that owns two mines. Mine B is smaller and has less capacity, thus its marginal costs rise more steeply than Mine A’s.

Mine A has TCa = 5000 + 50*qa + 2 qa^{2}

Mine B has TCb = 8000 + 50*qb + 3qb^{2}

a. Before knowing demand, can you tell whether the firm might choose to operate just one of the two mines? Explain.

b. Now assume inverse demand for the firm’s output is P = 1150 - Q.

Find optimal output at each plant, the monopolist’s total output, price, and profit or loss.

4. (3 pts) Jimbob’s Garage is the only auto repair facility in a remote area of the Nevada desert. The proprietor, Jimbob, does not post his prices for services. Knowing his customers are travelers who are desperate to get their vehicles repaired, he sizes each one up for their apparent ability to pay, and charges them accordingly.

Suppose annual demand for his repair services is Qd = 1000 - .5*P, and his marginal cost per repair job is $80. What is the range of prices he will charge his customers? How many cars does he repair per year? What is his profit if his fixed costs are $12,000/yr?

4. (5 pts). Cinemax is the only movie theater in Dannyburg. As such, it operates as a price-discriminating monopolist. Two types of customers view movies there: adults (A) and high school students (S) . Their respective demand functions are:

Qa = 6400 Pa^{-}^{2}

a. Without knowing marginal cost, what percent discount should the firm offer to students?

b. If the firm’s marginal cost per person is $4, what price should each type of ticket carry?

How many of each type of ticket are sold (round to nearest ticket if necessary)?

- 10 years ago

**ARE 100B HOMEWORK 1 (part a) Summer 2014 Solution**

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