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A monopolist faces a demand curve of the form: P = 610 – 0.01Q. The total...

A monopolist faces a demand curve of the form: P = 610 – 0.01Q. The total cost for this monopolist is TC = 2,000,000 + 10Q. Assume there are no externalities of production or consumption of this monopolist’s product.

a) Suppose this monopolist cannot price discriminate. Explain why this monopolist will not produce an output greater than 30,000 units.

b) Draw a diagram to illustrate this monopolist’s situation. Show the demand, marginal revenue and marginal cost curves, and the profit maximizing price and quantity from part (a).

Solutions

Expert Solution

a)

Given

P=610-0.01Q

Total Revenue=TR=P*Q=610Q-0.01Q^2

Marginal Revenue=MR=dTR/dQ=610-0.02Q

Total Cost=TC=200000+10Q

Marginal Cost=MC=dTC/dQ=10

Set MR=MC for profit maximization

610-0.02Q=10

0.02Q=600

Q=30000 units

Profit maximizing output is 30000 units.

If monopolist produces more than 30000 units say 30001 units,

Marginal Revenue=MR=610-0.02*30001=9.98

It means that MR is less than MC at this output level. It shows that net addition to profit (MR-MC) will be negative on the production of 30001th unit. So, monopolist will not produce any output more than 30000.

b)

Q      MR MC P
0 610 10 610
10000 410 10 510
15000 310 10 460
20000 210 10 410
25000 110 10 360
30000 10 10 310
30500 0 10 305

Rahul Sunny answered 8 months ago
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