Answer to Question #126028 in Microeconomics for Tshoanelo Mutembwa

Question

The television market in South Africa has two major suppliers producing differentiated television models. The monthly demand functions of the two suppliers is as follows:

Samsung q1= 450 - 2p1 + p2
LG q2 = 450 - 2p2 + p1

The marginal costs of production are R60 per unit and fixed costs are equal to zero

Part 1
a) write down an expression for Samsungs inverse demand function which expresses p1 on terms of q1 and q2 only

b) in a similar manner, write down the expression of LGs inverse demand function in the form of an equation for p2 in terms of q1 and q2 only

Answer 1

(a)

$p1=q2−450+2(q1−450+2p1)$

$p1=q2−450+2q1−900+4p1$

$3p1=1350−q2−2q1$

$p1 = 450 - \frac{1}{3} q2 - \frac{2}{3}q1$

(b)

$p2 = q1-450+2(q2-450-2p2)$

$p2=q1−450+2q2−900−4p2$

$3p2 = 1350 - q1 - q2$

$p2 = 450 - \frac{1}{3}q1 - \frac{2}{3} q2$