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Question 1: Monopoly A monopoly’s demand function is given by: D;P=160-2Q. It’s costs are given by:...

Question 1: Monopoly

A monopoly’s demand function is given by: D;P=160-2Q. It’s costs are given by: AC=MC=40. Calculate the firm’s profit.
Based on a. illustrate this market, including all intercepts, and calculate the deadweight loss caused by the monopolisation of this market.
The profit function for a second monopoly is given by: π=600Q-2Q3-1000. Calculate the firm’s fixed costs.
Using the profit function in c. calculate the firms profit if it firm produces 17 units.
Using the profit function in c. calculate the quantity of units this firm should produce in order to maximise profit.

Solutions

Expert Solution

(a) Given demand function is P = 160-2Q and AC=MC=40

So, the total revenue function is TR = P*Q = 160Q-2Q2 , and marginal revenue function is MR = dTR/dQ = 160-4Q

Total cost function is TC = AC*Q = 40Q

The profit of the monopoly is given by:

π = TR - TC = 160Q-2Q2-40Q = 120Q-2Q2

Profits are maximised at a point where dπ/dQ = 0 or MR = MC

Thus, 120-4Q = 0 or 160-4Q = 40

So, Qm = 30 and Pm = 160-2(30) = 100

and π = (120*30)-[2(30)2] = 3600 - 1800 = 1800

Qm = 30 , Pm = 100 and π = 1800.

(b) The monopoly in part (a) is shown below:

The monopoly equilibrium is depicted by em and perfect competition equilibrium is denoted by ec. The shaded triangle Aemec shows the deadweight loss (DWL) due to monopoly.

In perfect competition, P=MC

160-2Q=40

Qc = 60 and Pc = 40

Thus, DWL = area of triangle Aemec

= (1/2) * (Qc-Qm) * (Pm-Pc)

= (1/2) * (60-30) * (100-40) = (1/2)*30*60 = 900

DWL = 900

We know that π =TR-TC

The only constant term in the profit is '1000' that is it is not dependent on the quantity sold. Thus, these are the total fixed costs which the monopolist has to bear even if it is not producing any output.

TFC = 1000

(d) When Q=17

π = 600Q-2Q3-1000

= (600*17) - [2(17)3] - 1000

= 10200 - 9826 - 1000

= -626

Thus, at Q=17 units the monopolist is incurring a loss of 626.

π = -626

(e) To maximise the profits, the firt should produce at a point where

dπ/dQ = 0

d(600Q-2Q3-1000)/dQ = 0

600 - 6Q2 = 0

Q2 = 100

Q = 10

Thus, the monopolist should produce 10 units to maximise its profits.

Q = 10 units.

Rahul Sunny answered 1 year ago

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