Homework Answers
Answer:
A Profit maximizing price and quantity:
We will find MR first from TR
Q = 800 - 2P
2P = 800 - Q
P = 400 - 0.5Q
TR = 400Q - 0.5Q^2
MR = 400 - Q
We will find now MC
TC = 10000 + 50Q
MC = 50
MR = MC
400 - Q = 50
Q = 400 - 50 = 350
Putting Q = 350 in demand function to get value of P
350 = 800 - 2P
2P = 800 - 350
P = 225
Profit = TR - TC
= 350(225) - 10000 - 50(350) = 78750 - 27500 = 51250
B New price and quantity when C = 10000 - 70Q
MC = 70
MR = 400 - Q
MR = MC
400 - Q = 70
Q = 330
Putting Q = 330 in demand function to get value of P
330 = 800 - 2P
2P = 470
P = 235
Profit = TR - TC
= 330(235) - 10000 - 70(330) = 77550 - 33100 = 44450
When cost function in C = 10000 - 70Q, profit is reduced from 51250 to 44450. It is worse situation for company
C New price and quantity when C = 20000 - 50Q
MC = 50
MR = 400 - Q
MR = MC
400 - Q = 50
Q = 350
Putting Q = 350 in demand function to get value of P
350 = 800 - 2P
2P = 450
P = 225
Profit = TR - TC
= 350(225) - 20000 - 50(350) = 78750 - 37500 = 41250
When cost function in C = 20000 - 50Q, profit is reduced from 51250 to 41250. It is the worst situation for company.
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