Please explain the answers to part b and c 24.4 (0) A monopolist has an inverse
ID: 1105106 • Letter: P
Question
Please explain the answers to part b and c
24.4 (0) A monopolist has an inverse demand curve given by p(y) 2. 12 - y and a cost curve given by c(y) y (a) What will be its profit-maximizing level of output? 3 . b) Suppose the government decides to put a tax on this monopolist so that for each unit it sells it has to pay the government S2. What will be its output under this form of taxation? 2.5 (c) Suppose now that the goverhment puts a lump sum tax of $10 on the profits of the monopolist. What will be its output? 3Explanation / Answer
Demand: p = 12 - y
Cost: C = y2
(a) Profit is maximized by equating Marginal revenue (MR) & Marginal cost (MC).
Total revenue (TR) = p x y = 12y - y2
MR = dTR/dy = 12 - 2y
MC = dC/dy = 2y
Equating MR & MC,
12 - 2y = 2y
4y = 12
y = 3
p = 12 - 3 = $9
(b) A unit tax will lower effective price received by the firm (and increase MC of the firm) by $2 at every output level. New MC function becomes:
MC = 2y + 2
Equating MR & after-tax MC,
12 - 2y = 2y + 2
4y = 10
y = 2.5
(c)
A lump-sum tax is equivalent to a fixed cost of the monopolist, which is indeendent of level of output produced. Therefore it does not affect the marginal cost, and MC remains unchanged as in part (a). Therefore, the profit-maximizing condition is the same as in part (a), by equating MR & MC:
12 - 2y = 2y
4y = 12
y = 3