Question

You manage pricing at a small industrial parts manufacturer that competes with over one hundred other similar manufacturing companies. Each company’s products, including your 213B product, are somewhat differentiated because of the variation in quality and service provided by each company, and no single competitor dominates the market. Given your competitors’ current prices for similar products, the demand for your product number 213B is given by P=50-.02Q, where P is the price you charge per unit of this product and Q is the volume of production of this product per period. Your total costs for the product this period, including the total fixed cost for the 213B plant are given by TC=20,000+0.005Q^2. Your related marginal cost function is MC=0.01Q. a. (2 points) What is the marginal revenue function for this product? b. (4 points) What is your profit-maximizing level of output for this product? c. (4 points) What is your profit-maximizing price of this product? d. (4 points) What are your maximum total profits from this product? e. (6 points) Identify the market structure - perfect competition, monopolistic competition, oligopoly, or monopoly - described here. Based on your above findings, what do you expect to happen to your profit-maximizing price in the long run? What do you expect to happen to your maximum total profits in the long run? Briefly explain.

Answer 1

A.

P=50-.02Q

Multiplication of both the sides of the above equation with Q, will give revenue (R) function.

P*Q = R = 50Q - .02Q^2 ----------------------- (1)

Differentiation of above equation w.r.t. Q will give marginal revenue (MR) function.

dR/dQ = 50-.04Q

Or,

MR = 50-.04Q

B.

For profit maximizing level of output,

MR = MC

50-.04Q = .01Q

Q = 50/.05 = 1000

So, profit maximizing level of output is 1000.

C.

Profit maximizing price = 50-.02Q = 50-.02*1000 = $30

D.

Maximum total profit = Revenue – cost

Maximum total profit = 30*1000 – (20000 + .005*1000^2)

Maximum total profit = $5000

E.

It is a monopolistic competition as products are differentiated on the basis of quality and service delivery.

Price will come down and economic profit in the long run will be equal to zero. So, the firm will only be able to achieve the breakeven level in the long run.