Answer to Question #307079 in Economics of Enterprise for 1234

Question

The company produces alkaline batteries for two groups of consumers (poor and rich) whose inverse demand functions are below. MC=40. How many times should the number of poor consumers be greater than the number of rich consumers to justify the focus on the entire consumer surplus of the poor group?

P1 = 160 - 20Q;

P2 = 200 - 16Q

Answer 1

$P_1 = 160 - 20Q$

$TR = Q(160 - 20Q)$

$=160Q-20Q^2$

MR= 160-40Q

$P_2 = 200 - 16Q$

$TR= Q(200 - 16Q)$

$=200Q- 16Q^2$

$MR= 200-32Q$

For profit Maximization,

$MR=MC$

$160-40Q=40$

Q$_1$ = 3

$P_1 = 160 - 20(3)= 100$

$200-32Q= 40$

$Q_2= 5$

$P_2 = 200 - 16(5)= 120$

Number times = $\frac{5}{3}=1.67$