A monopolist faces an inverse demand function of both quantity, Q, and advertisi

Question

A monopolist faces an inverse demand function of both quantity, Q, and advertising effort, A, P(Q, A)=70-Q +A^1/2. The marginal cost of production is constant and 10, and the marginal cost of advertising is constant and 1. (a) What is the monopolist?s optimal choice of advertising and quantity? (b) What is the monopolist's profit given this optimal choice? (c) Find the optimal quantity given that advertising is equal to zero, A= 0. (d) Find profit. (e) Compare the profits from not advertising with the optimal advertising strategy.

Explanation / Answer

Ans)

a)

P(Q,A) = 70 – Q + A1 / 2

MCP = 10

MCA = 1

TC = 10Q +A

Now, max profit, = (70 – Q + A1 / 2 )Q - 10Q – A

d /dQ = 70Q – Q2 + A1 / 2 Q - 10Q – A

=>70-2Q+ A1 / 2-10 =0

=>60-2Q+ A1 / 2=0

d /dA = 70Q – Q2 + A1 / 2 Q - 10Q – A

            =>(1/2) A -1 / 2 Q -1 =0

=>Q*=40, A* =400

b) As above profit is given by:

= (70 – Q + A1 / 2 )Q - 10Q – A

Putting Q=40, A =800 in the above equation

= (70 – 40 + 4001 / 2 )40 – 10*40 – 400

= (70 – 40 + 20 )*40 – 800

= 1200

c) Now, max profit, = (70 – Q)*Q - 10Q

= 70Q – Q2 -10Q =0

= 60Q – Q2 =0

d /dQ = 60 – 2Q =0

Q = 30 units

d) = (70 – Q)*Q - 10Q

= 70Q – Q2 -10Q

= 60Q – Q2

= 60*30 – 302

= 900

e) The profits in the case of non- advertising reduces than from when the product is advertised.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.