Question

1. A firm called SoderWerks is a monopolist in the production of a sophisticated electronic device used in the construction of military tanks. It faces monthly market demand that varies according to the equation Q = 510 - 0.1P, where P is the price per device in dollars. The firm earns marginal revenue according to the equation MR = 5100 - 200 and incurs marginal costs according to the function MC = 1800 + 2Q, where Q is the quantity of these devices produced. a. How many of these devices will SoderWerks produce per month to maximize profit? What price will the firm charge per device? If SoderWerks incurs total costs according to the equation TC = 190,500 + 18000 + Q?, how much economic profit (or loss) will it earn selling this product in a typical month? c. Use the "algebraic formula" for elasticity to show that SoderWerks produces a level of output where demand is relatively elastic. d. At what level of output is the demand for this product unit elastic? e. At the profit-maximization point, is SoderWerks allocatively efficient? Explain.

Answer 1

a) A monopolist will produce using the rule MR = MC

5100 - 20Q = 1800 + 2Q

3300 = 22Q

Qm = 150 devices and price per device Pm = 5100 - 10*150= 3600

b) Profit / Loss = TR - TC = 3600*150 - (190500 + 1800*150 + 150^2) = 57000

c) We see that slope of the demand function is -0.1. Elasticity = slope of demand x price / quantity

= -0.1 x 3600/150 = -2.4 Since |ed| > 0, the demand is elastic.

d) ed = -1

-1 = -0.1 x P/Q

P = 10Q

Q = 510 - 0.1*10Q

or Q = 510 - Q

Q = 255. When Q = 255 and price = 2550, elasticity is -1.

e) No because it is not producing where P = MC but its level of output has MR = MC and since it is monopolist, its MR < Price.