Understanding Society

Topics: Supply and demand, Microeconomics, Economics Pages: 3 (432 words) Published: August 30, 2013
BSc (Hons)/MSc Business Economics and Investment Analysis
ECON 1007Y – Quantitative Methods for Financial Economics Tutorial 1

1. (i) When the demand function is 2Q – 24 + 3P = 0, find the marginal revenue when Q = 3. (ii) Given the demand function 0.1Q- 10 + 0.2p+0.02p2 = 0, calculate the price elasticity of demand when P= 10. (iii) If supply is related to price by the function p = 0.25Q+10, find the price elasticity of supply when p = 20. (iv) Given the demand function aQ + bP-k = 0, where a, b, and k are positive constants , show the price elasticity of demand is minus one when MR = 0.

2. (i) A firm’s total costs are 500 when output is 100. If the TC function is linear and fixed costs (FC) are 200, find the marginal cost when Q = 4, 5 and 6.

(ii) The following are estimates of TC and AC functions for various firms. Calculate the MC function in each case and say whether, or under what conditions, the MC function is economically meaningful.

a) AC = 20 + 3 +0.5Q
b) AC – 2 = 100 + 0.2Q
(c) TC – 100 – 2Q + 2Q2 = Q3
Give the MC when Q = 4 for (a), (b) and (c).

3.The market demand function of a firm is given by
4P + Q - 16 = 0
and the AC function takes the form

AC = 4 + 2 - 0.3Q + 0.05Q2
Find the Q which gives

i) maximum revenue
ii) minimum marginal costs,
iii) maximum profits

Use the second derivative test in each case.

4. A monopolist’s demand function is

P = 30 – 0.75Q

and his AC function takes the form

AC – 30 = 9 + 0.3Q Q
i) Find the Q which gives
a) maximum revenue,...
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