Chapter 8

Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of production is given by $C=200+2q^2$, where $q$ is the level of output and $C$ is total cost. (The marginal cost of production is $4q;$ the fixed cost is $\mathrm{\$}200.$ ) a. If the price of watches is $\mathrm{\$}100,$ how many watches should you produce to maximize profit? b. What will the profit level be? c. At what minimum price will the firm produce a positive output?

Suppose that a competitive firm's marginal cost of producing output $q$ is given by $\mathrm{MC}(q)=3+2q$. Assume that the market price of the firm's product is $\mathrm{\$}9$ a. What level of output will the firm produce? b. What is the firm's producer surplus? c. Suppose that the average variable cost of the firm is given by $\mathrm{AVC}(q)=3+q.$ Suppose that the firm's fixed costs are known to be $\mathrm{\$}3.$ Will the firm be earning a positive, negative, or zero profit in the short run?

A firm produces a product in a competitive industry and has a total cost function $C=50+4q+2q^2$ and a marginal cost function $\mathrm{MC}=4+4q$. At the given market price of $\mathrm{\$}20,$ the firm is producing 5 units of output. Is the firm maximizing its profit? What quantity of output should the firm produce in the long run?

Suppose the same firm's cost function is $C(q)=4q^2+16$ a. Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost. (Hint: Marginal cost is given by $\mathrm{MC}=8q$.) b. Show the average cost, marginal cost, and average variable cost curves on a graph. c. Find the output that minimizes average cost. d. At what range of prices will the firm produce a positive output? e. At what range of prices will the firm earn a negative profit? f. At what range of prices will the firm earn a positive profit?

A competitive firm has the following short-run cost function: $C(q)=q^3-8q^2+30q+5$ a. Find $\mathrm{MC},\mathrm{AC}$, and $\mathrm{AVC}$ and sketch them on a graph. b. At what range of prices will the firm supply zero output? c. Identify the firm's supply curve on your graph. d. At what price would the firm supply exactly 6

Suppose you are given the following information about a particular industry: \[ $$\begin{array}{ll}{Q}^D=6500-100P& \text{ Market demand }\\ Q^S=1200P& \text{ Market supply }\end{array}$$ \] \[ C(q)=722+\frac{q^{2}}{200} \quad \text { Firm total cost function } \] \[ M C(q)=\frac{2 q}{200} \quad \text { Firm marginal cost function } \] Assume that all firms are identical and that the market is characterized by perfect competition. a. Find the equilibrium price, the equilibrium quantity, the output supplied by the firm, and the profit of each firm. b. Would you expect to see entry into or exit from the industry in the long run? Explain. What effect will entry or exit have on market equilibrium? c. What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain. d. What is the lowest price at which each firm would sell its output in the short run? Is profit positive, negative, or zero at this price? Explain.

Suppose that a competitive firm has a total cost function $C(q)=450+15q+2q^2$ and a marginal cost function $MC(q)=15+4q.$ If the market price is $P=\mathrm{\$}115$ per unit, find the level of output produced by the firm. Find the level of profit and the level of producer surplus.

A number of stores offer film developing as a service to their customers. Suppose that each store offering this service has a cost function $C(q)=50+0.5q+0.08q^2$ and a marginal cost $MC=0.5+0.16q$ a. If the going rate for developing a roll of film is $\mathrm{\$}8.50$ is the industry in long-run equilibrium? If not, find the price associated with long- run equilibrium. b. Suppose now that a new technology is developed which will reduce the cost of film developing by 25 percent. Assuming that the industry is in longrun equilibrium, how much would any one store be willing to pay to purchase this new technology?

Consider a city that has a number of hot dog stands operating throughout the downtown area. Suppose that each vendor has a marginal cost of $\mathrm{\$}1.50$ per hot dog sold and no fixed cost. Suppose the maximum number of hot dogs that any one vendor can sell is 100 per day. a. If the price of a hot dog is $\mathrm{\$}2,$ how many hot dogs does each vendor want to sell? b. If the industry is perfectly competitive, will the price remain at $\mathrm{\$}2$ for a hot dog? If not, what will the price be? c. If each vendor sells exactly 100 hot dogs a day and the demand for hot dogs from vendors in the city is $Q=4400-1200P,$ how many vendors are there? d. Suppose the city decides to regulate hot dog vendors by issuing permits. If the city issues only 20 permits and if each vendor continues to sell 100 hot dogs a day, what price will a hot dog sell for? e. Suppose the city decides to sell the permits. What is the highest price that a vendor would pay for a permit?

A sales tax of $\mathrm{\$}1$ per unit of output is placed on a particular firm whose product sells for $\mathrm{\$}5$ in a competitive industry with many firms. a. How will this tax affect the cost curves for the firm? b. What will happen to the firm's price, output, and profit? c. Will there be entry or exit in the industry?