John, who is a terrific cook, has just started a restaurant. his inverse demand

Question

John, who is a terrific cook, has just started a restaurant. his inverse demand curve is equal to p(q) = 20-2q. her cost of production is given by TC(q) = ((q^2)/2) + 24

a) derive John's marginal revenue function. explain its two components
b) derive John's profit maximizing quantity of output and price for that output, as well as the profit when it is maximized.
c) John's fixed cost of 24 comes from a five year lease of the space where he has his restaurant. this lease is impossible to get out of. rumor has it that the landlord is about to double the rent, which would increase John's fixed cost of 48. would this change his quantity of output in the short run?

Explanation / Answer

a) Revenue= P8Q= (20-2q)*q = 20q-2q^2

Marginal revenue= 20-4q, 2 components are 20 (fixed) and 4q ( variable)

b) profit maximizing condition= MR=MC

Cost = (q^2)/2 +24 , MC = q

MR= 20-4q

so MR=MC; 20-4q=q; q= 4 is profit maximizing output,

profit = Revenue - cost ; at q=4, p= 20-2*4= 12; revenue= 12*4 =48; cost= (4^2)/2 +24 = 32; profit = 48-32= 16

c)when FC increases to 48; profit maximizing quantity remains constant at 4 as MC remains same as q.

profit = revenue- cost = 48- ((4^2)/2+48)= -8

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