Answer to Question #50826 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 the 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 this 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, Q = 2000 - 2P, MR=1000-Q
a) Total revenue is maximized, when marginal revenue MR = 0, so Q = 1000 units. The price elasticity of demand at Q = 1000 is Ed = (P/Q)(∆Q/∆P) = (500/1000)*(-2) = -1, so the demand is unit-elastic in this point. b) Q = 1000 units, P = $500. As Q and P are the same as in the previous question, the price elasticity of demand at this quantity is Ed = -1 too.
c) Muslim will sell no output, when P = 0. If the product were given away, Qd = 2000 - 2*0 = 2000.