QUESTION ONE
(a) Using game theoretic approach and given that the inverse demand function is P=a-qA+qB .
(i) Show that a firm that first enters the market will always have a larger markets share. (4marks)
(ii) What is the market price? (2marks)
(iii) What is the profit for the leader and follower? (2marks)
(iv) What is the industry profit? (1mark)
(v) What assumption have you made in (i) above? (2marks)
(b) (i) Show that trade in a perfectly competitive market will always
be a market Pareto efficient. (6marks)
(ii) Discuss the second theorem of welfare economics (4marks)
( iii) What are the policy implications of the second theorem of
welfare economies (4marks)
QUESTION TWO
(a) Prove that expenditure functions are concave in price. (3marks)
(b) Given a Cobb-Douglas utility function u(x1x2)=x10.5×20.5.
(i) Determine the Marshallian demand functions. (4marks)
(ii) The Hicksian demand functions. (4marks)
(b) Determine the Slutsky equation. (4marks)
QUESTION THREE
(a) Show that the effect of an income tax that raises same amount of
revenue as exercise tax will always achieve a higher level of utility
than excise tax. (5marks)
(b) Suppose initially a consumer has an income M0=100 and faces the
following prices of good x1 and x2: P10=P20=1, and e(p,u)= P10.5P20.5U.
If the government imposes a tax on the good x1 so that P1 rises to P1 1=4. What amount of additional income would be needed to compensate the consumer so that he remains on the same level of utility as before the imposition of the tax? (4marks)
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(c) “Asymmetric information is considered to be one of the causes of
market failure”. Using a relevant example, Discuss. (6marks)
QUESTION FOUR
(a) By an illustration, discuss the tragedy of the commons. (4marks)
(b) Distinguish between adverse selection and moral hazard (4marks)
(c) A risk-averse individual is offered a choice between a gamble
that pays Sh1000 with a probability of 25% and Sh100 with a probability of 75%, or a payment of Sh325. Which would he choose? (3marks)
(d) Draw a utility function that exhibits risk-loving behavior for
small gambles and risk-averse behavior for large gamble. (4marks)
QUESTION FIVE
(a) Given a cost function C(w,y)=2W10.5W20.5Y0.5.
(i) Determine the conditional input demand functions. (2marks)
(ii) Input demand function. (2marks)
(iii) Output supply function. (1marks)
(iv) Associated output function. (1mark)
(b)Find the cost function C(w,y), given that Y=min{x1/a1, x2/a2}. (3marks)
(c) Explain the concept of signaling. (3marks)
(d) If a stock has a β of 1.5, the return on the market is 10%, and the risk free rate of return is 5%, what expected rate of the return should this stock offer according to the capital asset pricing model? (3marks)
