Question #307079

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


1
Expert's answer
2022-03-07T11:04:52-0500

P1=16020QP_1 = 160 - 20Q

TR=Q(16020Q)TR = Q(160 - 20Q)

=160Q20Q2=160Q-20Q^2

MR= 160-40Q


P2=20016QP_2 = 200 - 16Q

TR=Q(20016Q)TR= Q(200 - 16Q)

=200Q16Q2=200Q- 16Q^2

MR=20032QMR= 200-32Q

For profit Maximization,

MR=MCMR=MC

16040Q=40160-40Q=40

Q1_1 = 3

P1=16020(3)=100P_1 = 160 - 20(3)= 100

20032Q=40200-32Q= 40

Q2=5Q_2= 5

P2=20016(5)=120P_2 = 200 - 16(5)= 120

Number times = 53=1.67\frac{5}{3}=1.67


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