Question

A monopolist faces a demand curve given by P = 200-10Q, where P is the price of the good and Q is the quantity demanded.  The marginal cost of production is constant and is equal to $60.  There are no fixed costs of production.

A)   What quantity should the monopolist produce in order to maximize profit?

B)   What price should the monopolist charge in order to maximize profit?

C)   How much profit will the monopolist make?

D)  What is the deadweight loss created by this monopoly (hint: compare the monopoly outcome with the perfectly competitive outcome).

E)   If the market were perfectly competitive, what would the price of the product be?

Answer 1

Answer:

A) Given

P=200-10Q

TR=P*Q=(200-10Q)*Q=200Q-10Q^2

MC=$60

for monopoly profit maximisation

MR=MC

MR=dTR/dQ=200-20Q

200-20Q=60

Q=7 Units

B)

P=200-10Q

So price when Q=7

P=200-10*7=$130

C) Profit =TR-MC*Q

Profit =P*Q-MC*Q

When Q=7 units

Profit =130*7-60*7=$490

D) for perfect competition price =MC for profit maximisaiton

P=$60

P=200-10Q

For P=60

Q=14 units

So dead weight loss= 0.5*(Perfect competition quantity-Monopoly quantity)*(Monopoly Price-Perfect competition Price)

dead weight loss=0.5*(14-7)*(130-60)=$245

E) For perfect competition Price =MC for profit maximizaiton

Price=$60

Answer 2

P = 200-10Q ,

MC = $60

A) A monopolist maximises his profit when Marginal revenue (MR) = Marginal cost (MC)

P= 200-10 Q

Total revenue = PQ = 200Q-10Q^2

Marginal revenue = 200-20Q

MC=$60

For profit maximisation = MR=MC

200-20Q= 60

140=20Q

Profit maximising quantity = Q= 7

B) P= 200-10Q

P= 200-7×10

P=200-70

Profit maximising Price level = $130

C) Profit = Total revenue - Total cost

Total cost = Marginal cost × Quantity

= 200Q -10Q^2 - 60Q

= 200×7- 10×7×7 - 60×7

=1400-490-420

=$490

D) Deadweight loss = shown in graph below

E) In a perfect competition profit maximisation point is where price = marginal cost

P = 200-10Q

Marginal cost = $60

For profit maximisation perfect competition price would be =

Price = MC

200-10Q = 60

200-60= 10Q

140= 10Q

Q= 14

price = 200-10×14

Price = 200-140

Price = 60

D)

Answer 3

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