The demand function for a rm’s product is Q(P) = 50 P/10 The rm’s cost of produc

Question

The demand function for a rm’s product is Q(P) = 50 P/10

The rm’s cost of production is C(Q) = Q3 20Q2 + 125Q

The rm’s problem is to choose the value of Q that maximizes its prot. You may occasionally nd an irrational number and in those cases simplify your answer as much as possible.

(a) Calculate the rm’s prot-maximizing price and quantity. Justify your answer carefully.

(b) Calculate the rm’s maximized prot, and the revenue and cost that produce that prot.

(c) Calculate the elasticity of demand at the prot-maximizing point.

Explanation / Answer

ANS a) Q AND P AT MAXIMUM PROFIT

Q= 15

P =500-10Q = 350

ANS b)

PROFIT, REVENUE AND COST AT PROFIT MAXIMISING POINT

TR= 500Q-10Q2 = 7500-2250 =5250

C = TC= Q3-20Q2+125Q = 3375 – 20 (225) + 1875 =3375 -4500+1875 =750

PROFIT= TR- TC =5250 -750 =4500

ANS c)

Q(P) = 50-P/10

ELASTCITY Ep = -(dQ/dP )* (P/Q)= - (-1/10) *(350/15) = 2.33

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