Answer to Question #185333 in Macroeconomics for HASAN ALI KHAN

Question #185333

If the demand function faced by a firm is:

Q = 90 – 2P

TC = 2 + 57Q – 8Q2 + Q3


Determine the level of output at which the firm maximizes the profit.


Determine the best level of output for the above question by the MR and MC approach.



1
Expert's answer
2021-04-28T09:34:26-0400

a) The firm will maximize profits at a point where MR = MC

TR = PQ = (45 - Q/2)×\times Q

=> MR = 45 - Q

TC = 2 + 57Q - 8Q2 + Q3

=> MC = 57 - 16Q + 3Q2

MR = MC

=> 45 - Q = 57 - 16Q + 3Q2

=> 3Q2 - 15Q + 12 = 0

=> Q2 - 5Q + 4 =0

=> Q2 - Q - 4Q + 4 =0

=> Q(Q-1) -4(Q-1) = 0

=> Q = 4 or Q = 1

Thus, the answer is Q = 4

b) Q = 90 – 2P

P=451/2QP=45-1/2Q

MR=dP/dQ=1/2MR=dP/dQ=-1/2

MC=dTC/dQ=5716Q+3Q2MC=dTC/dQ=57-16Q+3Q^2

Now MC=MR

5716Q+3Q2=1/257-16Q+3Q^2=-1/2

6Q232Q+115=06Q^2-32Q+115=0

On solving quadratically,

Q1=2.67and Q2Q_1=2.67 and \space Q_2 =2.67=2.67

so 2.67 is the best level of output


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