Answer to Question #42695 in Microeconomics for Ray

Question

The total demand for good Q is Made up by two markets demand. Market A displays a price elasticity of -2 whereas market B -4. The firm presents a cost function of the form : 120 + 4Q. Find the price charged by the firm in the two markets and the quantities supplied

Answer 1

Market A: EdA = -2
Market B: EdB = -4
TC = 120 + 4Q.

To find the price charged by the firm in the two markets and the quantities supplied, we should use markup rule. A markup rule refers to the pricing practice of a producer with market power, where a firm charges a fixed mark up over its marginal cost.

P = Ed*MC/(1 + Ed)
MC = TC' = (120 + 4Q)' = 4
So, price in market A equals PA = -2*4/(1-2) = $8
PB = -4*4/(1-4) = 16/3 = $5.33

According to the rule of profit maximization:

P'(Q)*Q + P - TC' = 0
P'(Q) = Ed, TC' = MC = 4, so:

-2QA + 8 - 4 = 0
2QA = 4, QA = 2 units.
-4QB + 5.33 - 4 = 0
4QB = 1.33
QB = 0.33 units