Question

1.Suppose the monopolist faces the market demand function given by2144PQ.The AVCof the firm is given as AVC = Q½andthe firm has a fixed cost of $ 5a)determine equilibrium P&Qb)determine the maximumprofit

2.Given Qd = 60–15P + P², the (point) price elasticity of demand at a price of 5

3Primary and secondary schooling is free in state schools in our country. If parents aregiven a choice of schools fortheir children, there will be a shortage of places in popularschools. What methods could be used for dealing with this shortage? What are theirrelative merits?

Answer 1

1. $Q = 144/P^2$ , $AVC = Q^{0.5}$ , FC = $5.

a) In equilibrium MR = MC.

$P = 12/Q^{0.5},$

$MR = TR'(Q) = 6/Q^{0.5},$

$TC = 5 + Q^{1.5},$

$MC = TC'(Q) = 1.5Q^{0.5},$

$1.5Q^{0.5} = 6/Q^{0.5}$

1.5Q = 6,

Q = 4 units,

P = 12/2 = 6.

b) The maximum profit is:

$TP = TR - TC = 6×4 - (5 + 4^{1.5}) = 11.$

2. Qd = 60 – 15P + P².

At a P = 5:

Qd = 60 - 15×5 + 25 = 10.

Q'd = -15 + 2P = -15 + 2×5 = -5.

The (point) price elasticity of demand is: $Ed = -5×5/10 = -2.5.$

So, the demand is elastic.

3. The priority for children living close to such schools may be set or additional payment for children who live in other towns or cities.