Question

Suppose demand function are                                                                                                                        

P₁ = 80 – 2.5Q₁

P₂ = 180 – 10Q₂

The Total Cost function is

TC = 50 + 40Q

find the price of two markets and amount of output to be sold in each market so that profit is maximized. Also find the total profit to be made from the strategy of price discrimination.

Answer 1

$$Solution$$

Let's find the optimal sales to the first $q_1$ and to the second $Q_2$. Remember to achieve this the $MR=MC$

$TC=50+40Q\\ MC=40\\ But\ Total\ Revenue=P*Q\\ Q(80-2.5q_1)=80q-2.5q_1^2\\ Determine, MR\\ =80-5q_1\\ But\ MR=MC\\ 80-5q_1=40\\ q_1=8\\ Therefore; P_1=80-2.5(8)\\ =60$

$P_2;\\ TR=P_2*Q\\ Q(180-10Q)\\ =180q-10q_2^2\\ MR=180-20q_2\\ but\ MR=MC\\ 180-20q_2=40\\ q_2=7\\ Therefore;\ P_2=180-10(7)\\ =110$