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1. Preferences and Utility
a. Bob enjoys cookies (x) according to the utility function U(x)=20x- 2 tx , where t is a
parameter that reflects how hungry he is. Cookies are costless in Bob’s world and so there is
no income constraint. Using the envelope theorem, calculate how Bob’s maximum utility
from eating cookies varies with t.
b. Are the following utility functions quasi-concave? Show why
i. 𝑈(𝑋, 𝑌) = ln(𝑋) + ln(𝑌)
ii. 𝑈(𝑋, 𝑌) = min(𝑋, 𝑌) (Hint: You can use a diagram or sample values here)
2. Utility Maximization
A consumer faces income constraints and has CES preferences of the following form:
U(x, y) x y
a. Find the consumer’s demand for x as a function of prices and income.
b. Are these preferences homothetic? Explain why or why not.
c. Calculate the consumer’s income elasticity of demand.
primary and secondary schooling is free in our country . if parents are given a choice of schools for their children,there will be a shortage of places in popular schools.what method could be used for dealing with this shortage? what are their relative merit?
What is the economic profit earned or loss incurred by the firm?
c. Based on your answers of (a) & (b) determine if the firm should shut down or operate in the
short run. Explain your answer.
d. Based on your answers of (a) & (b) determine what should be the firm's decision regarding exit in the long run. Explain your answer.
A competitive firm’s cost function is given as C = 100q − 4q 2 + 0.2q 3 + 450. When the market price is 75, what will the firm do in the short run? Draw a diagram that includes MC, AC, and AVC curves, and indicate the area for the profit in case the firm decides to produce.
Suppose that there are two types of firms in a perfectly competitive market. Firms
of type A have costs given by CA(q) = 30q2 + 10q. Firms of type B have costs given by CB(q) = 50q2 + 10.
( dCA
dq = 60q + 10 and dCB
dq = 100q). There are 60 firms of type A and 100 firms of type B.
(A). [5 Points] Derive the individual firm supply functions for each type of firm qs
A(p) and qs
B(p). What
is the range of prices in which some firms produce but others do not? Are there prices at which no firms
produce? Why?
for rice by 10%. Calculate her income elasticity of demand for rice using point elasticity metho
1) If the total utilities for the fifth and sixth units of a good consumed are 98 and 115 respectively. The marginal utility for the sixth unit is:
How does adidas manage their cost of production and became successful?
(a) What are indifference curves? illustrate any three peculiar shapes that can be taken by indifference curves 6 mks
What is oligopoly? Explain the assumptions of an oligopolistic market (6 mks)
The government of Kenya imposes a binding quota of q* on steel imports. suppose the supply curve is relatively inelastic while the supply curve of foreign supplier is very elastic. use a figure to show the effect of the quota on the Kenya price of steel, the quantity of steel sold by Kenyan firms, and the total quantity sold within the country. 4mks
