Please answer with readable text & explain your answers. Question 2 (25 points):

Question

Please answer with readable text & explain your answers.

Question 2 (25 points): (Advertising) A monopolist produces a product whose price and production costs vary with advertising A and quantity q according to P(A,A(1- q) 1) Calculate the equilibrium price and advertising levels that a monopolist would choose, and the corresponding quantity sold. 2) Derive the consumer surplus CS(A, q) for any combination of A and q 3) Now fix A 1/2 and let the monopolist be a public firm. Calculate the equilibrium production level of the monopolist that aims to maximize the social surplus (Consumer surplus+producer profit)

Explanation / Answer

For Monopolist

MR=MC

R=A(1-q)*q=Aq-Aq^2

MR=A-2Aq

MC=A^2

A-2Aq-A^2=0

A(1-2q)=A^2

1-2q=A

(1-A)/2=q

P=A(1-q)=(1-2q)(1-q)=1-3q+2q^2

When P=0, q=1

CS=0.5(2q^2-3q+1)((1-A)/2-1)=(q^2-1.5q+0.5)((1-A)/2-1)

If A=1/2

then q=1/4

Price=P=A(1-q)=(1-2q)(1-q)=1-3q+2q^2=0.375

CS=0.5(2q^2-3q+1)((1-A)/2-1)=(q^2-1.5q+0.5)((1-A)/2-1)=-0.140625

Profit=Revenu-Cost=0.375*0.25-(0.25*0.25)=0.03125

Social welfare=-0.140625+0.03125=-0.109375

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