Download Mathematical Economics List 4 1. Given a firm`s production level q

Mathematical Economics
List 4
1. Given a firm's production level q, its total production costs are given by
CT(q) = 400 + 2q + 0,01q2
The firm operates in a perfectly competitive market.
a) Derive the i) average cost function, ii) marginal cost function.
b) Derive the minimum average costs and the corresponding level of production.
c) Derive the production curve.
2. Consider a market subject to the laws of perfect competition. The demand and supply
functions are given as follows:
qd = 600 – 30p;
qs = 20p – 200.
i) Derive the equilibrium price and demand.
ii) A tax of δ per unit sold is imposed. Derive the new equilibrium (shop) price and demand.
3. Assume that the total production costs of a monopoly producing q units of a good are given
by CT(q) = 400 + 2q + 0,01q2
The demand function is given by qd = 2000 – 100p.
i) Derive the price and level of production which maximize the monopoly's revenue, together with
the corresponding revenue.
ii) Derive the price and level of production which maximize the monopoly's profit, together with the
corresponding profit.
iii) A tax of 1 per unit sold is imposed. Derive the new (shop) price and level of production which
maximize the monopoly's profit, together with the corresponding profit.
4. The the system of income taxation applied in Ruritania is described in the following table
(in Ruritanian dollars).
From
To
Marginal Rate (%)
0
10 000
0
10 000
40 000
10
40 000
80 000
25
80 000
∞
40
a) Determine the amount of income tax to be paid when income is: i) $25 000, ii) $75 000,
iii) $140 000
b) Determine the average tax rate in these three cases.
c) A worker makes use of tax relief. If he earns $100 000, he would pay $15 000 tax. If he earns
$110 000, then he would pay $17 800. Estimate his marginal tax rate.