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

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

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.

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 1 month ago

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