Questions 1 and 2 are independent of each other. 1. Complete the following table

Question

Questions 1 and 2 are independent of each other. 1. Complete the following table and find the monopoly price and quantity. Q P TR MR TC MC Profits 0 36 0 1 3333 2 3060 3 27 81 4 24 96 5-21-T-105 47 48 50 54 62 78 2. Demand is defined by Qd-2-P/5 and total cost is defined by TC-32. (a) What is the monopoly solution, QM, pMr)? (b) What is the producer surplus, consumer surplus, welfare, and deadweight loss cor- responding to the monopoly solution? (c) Sketch the monopoly solution and shade the area corresponding to the monopoly profits

Explanation / Answer

Question 1

Marginal revenue is calculated as follows -

MR = Change in total revenue/Change in output

When output increases from 0 to 1, total revenue increases from 0 to 33.

So,

Change in total revenue = 33 - 0 = 33

Change in output = 1 - 0 = 1

MR = Change in TR/Change in Output = 33/1 = 33

Similarly, MR at other levels of output can be calculated.

Marginal cost is calculated as follows -

MC = Change in total cost/Change in total output

When output increases from 0 to 1, total cost increases from 47 to 48.

So,

Change in total cost = 48 - 47 = 1

Change in output = 1 - 0 = 1

MC = Change in total cost/Change in output = 1/1 = 1

Similarly, MC at other levels of output can be calculated.

Following is the complete table -

A monopolist maximizes profit when it produce that level of output corresponding to which MR equal MC.

If there is no such output in explicit terms then monopolist maximizes profit by producing that level of output up to which MR>MC.

Up to production of 4 units, MR is greater than MC.

Price corresponding to 4 units is $24.

So,

The monopoly price is $24 per unit.

The monopoly quantity is 4 units.

Q P TR MR TC MC Profit 0 36 0 - 47 - -47 1 33 33 33 48 1 -15 2 30 60 27 50 2 10 3 27 81 21 54 4 27 4 24 96 15 62 8 34 5 21 105 9 78 16 27

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