Question

Suppose that a Monopolist's market demand is given by P a - Q, a>2, and that the a) Calculate the profit maximising monopoly price and quantity. b) Calculate the price and quantity that arise under perfect competition. [8 marks ] c) Calculate and compare Consumer and Producer Surplus both under monopoly [6 marks ] and perfect competition: what is the Deadweight loss due to Monopoly? Provide a graphical description of the two cases. [16 marks]

Answer 1

Given, P = a - Q

TR = aQ - Q²

MR = a - 2Q

MC = 2

A. Monopolist will maximize profit by satisfying the following relationship

MR = MC

a - 2Q = 2

$\large 2Q = a - 2$

$\large Q = \frac{a - 2}{2}$( where a>2)

P = a - Q

$\large P = a -\frac{a - 2}{2}$

$\large P = \frac{2a - a + 2}{2}$

$\large P = \frac{a + 2}{2}$

Profit maximizing price = (a+2)/2

Profit maximizing quantity = (a-2)/2

B. In case of perfect competition the firm will maximize its profit by equating price with marginal cost

P = MC

a - Q = 2

Profit maximizing quantity, Q_P = a - 2

Profit maximizing price, P_P = a - (a -2) = $ 2 per unit

C. Monopoly

Consumer Surplus

$\large CS = \frac{1}{2}*(a-\frac{a+2}{2})* \frac{a-2}{2}$

$\large CS = \frac{(a-2)^2}{8}$

Producer surplus

$\large PS = (\frac{a+2}{2}-2)*\frac{a-2}{2}$

$\large PS = \frac{(a-2)^2}{4}$

Dead weight loss

$\large DWL =( {\frac{a+2}{2}-2})*(a-2 - \frac{a-2}{2})$

$\large DWL =(\frac{a-2}{2})^2$

Perfect Competition

2 LC 0

Consumer Surplus

$\large CS =\frac{1}{2}*(a-2)(a-2)$

$\large CS =\frac{(a-2)^2}{2}$

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