Question #304822

Q2: Marres limited has the following demand and cost functions



Demand function: P=80-3Q, where P is the unit selling price and Q is quantity in thousands



Cost function: TC=Q2+20Q+100, where TC is total cost in Ksh 000000



Required:



Optimal price to maximize profit (3mks)



Maximum profit (2mks)

1
Expert's answer
2022-03-02T17:04:04-0500

Given that:

TC=Q2+20Q+100TC=Q^2+20Q+100 and

P=803QP=80-3Q

TR=P×QTR=P×Q

TR=(803Q)Q=80Q3Q2TR=(80-3Q)Q=80Q-3Q^2

TR=MR=806QTR'=MR=80-6Q

TC=MC=2Q+20TC'=MC=2Q+20


MR=MCMR=MC at equilibrium

Then:

806Q=2Q+2080-6Q=2Q+20

8Q=608Q=60

Q=7.5Q^*=7.5 in thousand


a) Optimal price to maximize profit:

P=803(7.5)=Ksh57.5P^*=80-3(7.5)=Ksh57.5


b) Maximum Profit, π\pi =TRTCTR-TC

At Q=7.5Q^*=7.5

π=80(7.5)3(7.5)2((7.5)2+20(7.5)+100)\pi=80(7.5)-3(7.5)^2-((7.5)^2+20(7.5)+100)

π=125(Ksh000000)\pi=125(Ksh '000000)


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