Answer to Question #52119 in Microeconomics for Asif

Question

Muslim Glass Company faces the following demand and marginal revenue functions:
P=1000-0.5Q, MR=1000-Q
P is the price, Q is quantity and MR is the Marginal Revenue.
a) At what quantity is total revenue maximized? what is the price elasticity of demand at this quantity?
b) The firm has been selling 1000 units per period at a price of $500. What is the price elasticity of demand at t his quantity?
c) At what price would Muslim sell no output? What quantity would be demanded if the product were given away?

Answer 1

P=1000-0.5Q, Qd = 2000 - 2P, MR=1000-Q
a) Total revenue is maximized, when MR = 0 and Q = 1000 units. The price elasticity of demand at this quantity is Ed = P/Q*Qd' = 500/1000*(-2) = -1, so demand is unit-elastic.
b) If the firm has been selling 1000 units per period at a price of $500, the price elasticity of demand at this quantity is Ed = P/Q*Qd' = 500/1000*(-2) = -1, so demand is unit-elastic.
c) Muslim would sell no output, when P = 1000 - 0.5*0 = $1000.