ECONOMICS (HONS) – SEM-III
INTERMEDIATE MICRO-I
Maximum Marks : 75
Time : 3 Hours
PART-I
Instruction : Attempt any three questions
1.
(a)
Plot the indifference maps for each of the following preference
ordering:
(i)
I only like grapes and never eat banana
(ii)
Arit’s marginal rate of substitution of food for clothing is 3/2,
no matter how many units of each he currently consumes.
(iii)
Ux, y  x 2  xy  y 2
(iv)
Ux, y  x  logy
(v)
Plot the indifference curve of a miser, relating money and all
other goods.
5
(b)
Let u(x, y) = max[2x, y] and assume that the price of both
commodities is equal to Rs. 1 Derive the Income Other Curve and the
Engel Curve for commodity x.
5
(c)
When prices are (4, 6), Goldie chooses the bundle (6, 6), and when
prices are (6, 3), she chooses the bundle (10, 0).
Is Goldie’s behavior consistent with the weak axiom of revealed
preference?
5
2.
(a)
Consider the utility preference function U  Y  4 X
(i)
What is the shape of the indifference curve. Show diagram.
(ii)
Given M = 200; Px =4; Py =5, find equilibrium constant of X and
Y
(iii)
What happens when Px falls to Rs. 2.
Find the price effect, substitution effect and Income effect.
5
(b)
Show using indifference curve analysis that lump sum subsidy makes
the consumer better off as compared to the excise subsidy which
costs the government the same amount.
5
(c)
Draw a representative diagram showing POC and demand curve of an
individual with following utility functions.
(i)
U = Min(x, y). What can you say about the price elasticity of
demand of commodity x?
(ii)
U=x+y
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3.
(a)
(b)
(c)
Mani has an income of 1,00,000 this year and she expects an income
of Rs. 2,24,000 next year. She stays in a village where there is no
banking facility but she can lend money to fellow villagers at an
interest rate of 4% p.a. Consumption goods cost Re.1 per unit this
year and there is no inflation. Her utility function over the two years
is UC1 , C2   C12C32 where C i represents the value of consumption in
ith year.
(i)
Draw the intertemporal budget line
optimum consumption bundle.
and determine the
(ii)
Suppose a bank is instituted in the village which gives an
interest of 4% p.a. on deposits and charges 12% p.a. on
borrowings. Draw the intertemporal budget line. Find optimum
consumption bundle and compare the result with part (a) in
welfare terms.
5
Suppose Milkha Singh likes milk and eggs as they helps him to run
faster. The satisfaction he gets from 2 cups of milk is same as 3 eggs
irrespective of his consumption level. A cup of milk is available for Rs.
5 and eggs are sold at Rs. 24 per dozen
(i)
Write down two possible utility functions that represents his
preferences and explain why they represent the same
preferences.
(ii)
If he was given Rs. 250 for buying milk and eggs, what would
be his consumption bundle?
5
The owner of an egg farm produces 300 eggs a week. Initially the price
of eggs is Rs. 4 per egg. Her demand function for eggs, for her own
consumption is :
x  180 
m
10P
Where x is the number of eggs she consumes per week, P is the price
of an egg and m is her income. The price of eggs then falls to Rs. 3 per
egg. How many eggs does she consume before and after the fall in
price of eggs? How much is the SE, IE & endowment income effect on
her consumption of eggs?
5
4.
(a)
Workout the present value of an income stream which gives a
constant income return of R every year starting from the end of year
5. It is perpetual bond and assume discount rate to be 10%.
5
(b)
Wendy and Mac work in fast food restaurants. Wendy gets $4 an hour
for the first 40 hours that she works and $6 an hour for every hour
beyond 40 hours a week. Mac gets $5 an hour no matter how many
hours he works. Each has 80 hours a week to allocate between work
and leisure and neither has any income from sources other than
labor. Each has a utility function U = cr, where c is consumption and
r is leisure. Each can choose the number of hours to work.
(i)
How many hours will Mac choose to work?
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(ii)
(c)
Will Wendy choose to work overtime? What is the best choice
for Wendy? How many hours a week will she work?
5
Shweta wants to sell a small chocolate factory located close to a river
that occasionally floods. If there is no flood, the factory will be worth
Rs. 40,000. If there is flood, then what is left of factory will be worth
only Rs. 1600. She thinks that the probability that there will be flood
is 25%. Shweta’s utility function is UC   C where C denotes the
contingent commodity rupees.
(i)
Compute her expected consumption, expected utility, the
certainty equivalent and the risk premium of the risky
outcome.
5
PART-II
Instruction : Attempt any two questions
5.
(a)
Can the long run total cost curve of a firm be a positively sloped
straight line through the origin? What does it imply? What shapes will
the long run average cost and long run marginal cost take in this
case? Can the short run average cost be U-shaped?
5
(b)
Let output be given by the following production function
Q = min (5K, 10L)
Where K is capital and L is labour. Let price of capital be Re. 1 per
unit and price of labour be Rs. 3 per unit. If only 10 units of capital
are employed, find the short run total cost.
5
(c)
Define elasticity of substitution.Calculate it for following production
function(i) q  f k, l   min ak, bl
(ii) q  f k, l   k α l β
(iii) q  f k, l   ak  bl
6.
(a)
5
The production of computers for company A is given by Q  10 KL . A
competitor company B uses the production function Q  10K 0.6 L0.4
7.
(i)
If both companies use equal amounts of K and L, which
company generates more output.
(ii)
Assume that K is a machine hours, but labor is unlimited in
supply. In which company is MPL the greater. Explain.
5
(b)
Write cost function for following production function :
(c)
(i) q  f k, l   min ak, bl (ii) q  f k, l   k α l β (iii) q  f k, l   ak  bl 5
What is expansion path? Derive cost function from expansion Path. 5
(a)
A Los Angeles firm uses a single input to produce a recreational
commodity according to a production function f x   4 x , where x is
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the number of units of input. The commodity sells for $100 per unit.
The input costs $ 50 per unit.
(b)
(i)
Write down a function that states the firm’s profit as a function
of the amount of input.
(ii)
What is the profit-maximizing amount of input & output? How
much profits does it make when it maximizes profits?
(iii)
Suppose that the firm is taxed $20 per unit of its output and
the price of its input is subsidized by $10. What is its new
input level? What is its new output level? How much profit does
it make now?
5
A firm has two variables factors and a production function,
1/4
f x1 , x 2   x1/2
1 x 2 . The price of its output is 4. Factor 1 receives a wage
of w1 and factor 2 receives a wage of w 2 .
(i)
Write an equation that says that the value of the marginal
product of factor 1 is equal to the wage of factor 1 and an
equation that says that the value of the marginal product of
factor 2 is equal to the wage of factor 2. Solve two equation in
the two unknowns, x1 and x 2 , to give the amounts of factors 1
and 2 that maximize the firm’s profits as a function of w1 and
w2.
(ii)
(c)
If the wage of factor 1 is 2, and the wage of factor 2 is 1, how
many units of factor 1 will the firm demand? How many units
of factor 2 will it demand? How much output will it produce?
How much profit will it make?
5
“Input demand functions are unambiguously downward sloping”.
Explain in terms of the Substitution and Output Effects using the
graphical approach.
5
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