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Microeconomic Theory 3 Question Paper

Microeconomic Theory 3

Course:Bachelor Of Arts (Economics & Sociology)

Institution: Kenyatta University question papers

Exam Year:

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2011/2012
SECOND SEMESTER EXAMINATIONS FOR THE DEGREE OF BACHELOR OF ECONOMICS
EET 300: MICROECONOMIC THEORY 111
DATE; Friday 30th March 2012 TIME: 4.30P.M-6.30pm
Instructions: Answer question one and any two questions
Question One
Write brief notes on the following concepts. Be as precise as you can. (5 marks each)
a) The production function
b)The Hoteling’s lemma
c) Elasticity of substitution
d) The Roy`s identity
e) The slut-sky `s equation
f)The Carnot equilibrium
QUESTION TWO
a) State the shepherd`s lemma and briefly explain its usefulness. (5 Marks)
b)A maize farmer produces using two inputs labour,(L), and fertilizer,(K), the farmers total cost function is given by TC=(0.5r+rw1/2+0.5w)q where q is output of maize in bags and r and w are the unit prices of fertilizer and labour respectively. Fertilizer is measured in bags. If the farmer`s objective is to produce 10,000 bags of maize, and fertilizer costs kshs 1600 per bag and labour costs kshs 100 per hour, how many bags of fertilizer will the farmer require to minimize cost?
c) Given the above cost function for the farmer, obtain the corresponding production function.(10 Marks)
QUESTION THREE
a) The profit function is said to be convex and positively linearly homogeneous in both input and output prices. Consider the candidate profit function below:
p(p,w)= Pr/w1sw2t where p is output price and w1 and w2 are the prices of two inputs x1 and x2 respectively. For what values of r,s and t is the above profit function legitimate? (15 Marks)
b) Suppose r=3, s=t=1.If p=sh 500, w1=w2=sh 100, determine the profit maximizing input demands and output.(10 Marks)
QUESTION FOUR
You are provided with the following indirect utility function
V(P,M) =[P12+P22]-1/2M where p1 and p2 are the prices of two goods x1 and x2 respectively, and M is the consumers income. Required;
(i) Derive the consumers expenditure function (2 Marks)
(ii) Find the uncompensated demand function for good x1 (4 Marks)
(iii) Find the compensated demand function for good x1 (4 Marks)
(iv) State and demonstrate the slutsky`s equation (10 Marks)

QUESTION FIVE
a) Along run cost function for each firm in a competitive industry is given as:
c(q)= q3/3 -2q2+13q ,where q represents output. The market demand for the product is given as q=1250-50p, where p is the unit price of output in shillings.
i) Determine the equilibrium output for each firm in the industry (2 Marks)
ii) What is the optimal number of firms in the industry? (2 Marks)
iii) Suppose a quantity tax of ksh 6 is imposed in the market, what will be the optimal number of firms in the industry?

b)A duopoly industry faces a linear inverse demand function given by P=100-Y,where Y=Y1+Y2,and Y1 and Y2 are the outputs by firms 1 and 2 respectively. The cost functions for the two firms are C1=10Y1 and C2=Y22/2.
i)Suppose firm 1 is a quantity leader, find the equilibrium price and quantities in the industry.(4 Marks)
ii) Suppose firm 1 is a price leader, how would the answer`s in (i) above change?(4 Marks)
iii) Suppose the two firms colluded to maximize their joint profits, how much would each produce, and at what price would profits be maximized? (6 Marks)

Microeconomic Theory 3 Question Paper

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