sample questions of ISI ME 2 , 2010

[vishruti]

QUESTION 1

(a) Imagine a closed economy in which tax is imposed only on income. The
government spending (G) is required (by a balanced budget amendment
to the relevant law) to be equal to the tax revenue; thus G = tY , where t
is the tax rate and Y is income. Consumption expenditure (C) is proportional
to disposable income and investment (I) is exogenously given.

(i) Explain why government spending is endogenous in this model.

(ii) Is the multiplier in this model larger or smaller than in the case in
which government spending is exogenous?

(iii) When t increases, does Y decrease, increase or stay the same? Give
an answer with intuitive explanation.

(b) Consider the following macroeconomic model with notation having usual
meanings: C = 100 + 1.3Y (Consumption function), I = 500
r (Investment function), MD = 150Y +100−1500r (Demand for money function)
and MS = 2100 (Supply of money). Do you think that there exists an
equilibrium? Justify your answer using the IS-LM model.

[vishruti]

Answer 1
 
a) (i)  since G = tY , so its dependent on Y , which is determined by the model , hence G is endogenous
 
(ii) the multiplier in this model is smaller than the usual model. In this model the multiplier is 1 /[ 1 + t - c ( 1 - t ) ] and the usual multipplier is 1 / [ 1 - c(1 - t) ]
 
(iii) as t increses Y will decrease , we can calculate dY / dt which is negative
 
b) solution does not exist because when we solve the two equation we get r = -104/503 and Y = 17000/1509. But we cannot have a negative value for the interest rate.

[vishruti]

Consider a market with two firms. Let the cost function of each firm be
C(q) = mq where q  0. Let the inverse demand functions of firms 1 and 2 be
P1(q1, q2) = a − q1 − sq2 and P2(q1, q2) = a − q2 − sq1, respectively. Assume
that 0 < s < 1 and a > m > 0.

(a) Find the Cournot equilibrium quantities of the two firms.

(b) Using the inverse demand functions P1(q1, q2) and P2(q1, q2), derive direct
demand functions D1(p1, p2) and D2(p1, p2) of firms 1 and 2.

(c) Using the direct demand functions D1(p1, p2) and D2(p1, p2), find the
Bertrand equilibrium prices

[Benhur]

dis ques has been answered in another forum...check it out

[vishruti]

QUESTION 3

(a) A monopolist can sell his output in two geographically separated markets
A and B. The total cost function is TC = 5 + 3(QA + QB) where QA
and QB are quantities sold in markets A and B respectively. The demand
functions for the two markets are, respectively, PA = 15 − QA and PB =
25 − 2QB. Calculate the firm’s price, output, profit and the deadweight
loss to the society if it can get involved in price discrimination.

(b) Suppose that you have the following information. Each month an airline
sells 1500 business-class tickets at Rs. 200 per ticket and 6000 economyclass
tickets at Rs. 80 per ticket. The airline treats business class and
economy class as two separate markets. The airline knows the demand
curves for the two markets and maximizes profit. It is also known that
the demand curve of each of the two markets is linear and marginal cost
associated with each ticket is Rs. 50.

(i) Use the above information to construct the demand curves for economy
class and business class tickets.

(ii) What would be the equilibrium quantities and prices if the airline
could not get involved in price discrimination?

[Benhur]

ans to a)

pA=9
pB=14
QA=6
QB=5.5

therefore total profit is 91.5

deadwt loss is 559/4

i m nt much sure abt d deadwt loss though..


ans to b)

i)
demand curve for buisness class is
P= 350 - 0.1Q

demand curve for class is
P=110 - (1/200)Q

ii)
in case of no price discrimination

output is 12750
price is 425/7

[priyanka p]

hi Benhur ,    my answers to part (a) are same as urs except i dont know how to calculate dead wt. loss, please explain d same.      and for (b) part, i got the same dd fns but  the second part answers are not same, i must have comitted some mistake. could u pls just give the equations used to get the eql qty and price. thanx

[priyanka p]

ans 3 part(b) 2nd part, i am getting answers q=7500 and p=18000/210               what i did is  taking 2 eqns    q1= 3500-10p1       and   q2=22000-200p2        taking single price p and adding both eqns i get  total Q= 25500-210p    therefore getting inverse dd fn as p=2550/21 - q/210   now calculating MR and equating it to MC that is 50, i get my answers.   PLS TELL ME WHERE AM I WRONG. THANX

[Benhur]

3 b) 2nd part i did the same thing...i got d same demand funcs...yes u r rite..i made a mistake..i took d MC=0...yes even m gettng 7500 and 600/7

[Benhur]

dead wt loss is d sum of consumer surplus and producer surplus...

producer surplus is the area under the supply curve and the equilibrium price..in dis case the producer surplus is the total profit

consumer surplus(CS) is the area under the demand curve from the equilibrium price..(ie if u draw the graph with demand curve and a horizontal line as the price,the upper triangle is the consumer surplus)..

CS for A=0.5X(6)X(15-9)

6 is the base ie equi output
15-9 is the height of the triangle where 15 is the vertical intercept and 9 is the equi price.

similarly CS for B=0.5X(11/2)(25-14)

therefore total CS is 193/4

profit ie total producer surplus is 91.5

adding we get the deadwt loss as 559/4

[priyanka p]

thank you so much benhur. which clg r u from and which year?

[Benhur]

i am from presidency...kolkata..m in 3rd year..will give isi entrance dis week..

[Benhur]

now lets solve the 4th question...

[priyanka p]

4 (a) i got p1/p2= (T/K)(X1/X2)    and for (b) it shuld increase

On Mon, May 3, 2010 at 10:41 AM, Benhur [via Discussion forum] <[hidden email]> wrote:

now lets solve the 4th question...

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[vishruti]

Answer 2
 
a) q1 = q2 = [a - m ] /[ 2 + s ]
 
b) direct demand functions are
 
q1 = ( a/1+s ) - ( p1 / 1 - s^2 ) + (sp2 / 1 - s^2)
 
q2 = (a/1+s) - ( p2/1 - s^2 ) + (sp1 / 1 - s^2)
 
c) p1 = p2 = [(1-s)a + m] / [s + 2]

[sonal]

hi priyanka can u explain hw u solved 4a)

[sonal]

vishruti-----the ans to 2c)is (a+m)(1-s)/(2-s).plz check....2a) and b) are correct
priyanka----can u tell me hw to derive the demanf func in Q3...its easy,bt i think i'm missing out a pt.
benhur-----isn't deadweight loss in monopoly the loss in the total surplus(consumer+producer) as compared to the competitive outcome?in market A we'l get 1/2.6.6=18 and in market B we'l get 1/2.11.11/2=121/4....plz tell me if this logic is wrong....

[vishruti]

Thankyou sonal for correcting me

but there is an error in your answer as well...

i recalculated , p1 = p2 = [ (1-s) a + m ] / [ 2 - s ]

[vishruti]

The answer given by behnur for third question part a and b i is correct and the by priyanka for the third question part b ii is correct

Thankyou!

[vishruti]

QUESTION 8

Consider a Solow model with the production function Y = K^1/2L^1/2, where Y ,
K and L are levels of output, capital and labour, respectively. Suppose, 20% of
income is saved and invested. Assume that the rate of growth of labour force is 0.05.

(a) Find the capital-labour ratio, rate of growth of output, rate of growth of
savings and the wage rate, in the steady state growth equilibrium.

(b) Suppose that the proportion of income saved goes up from 20% to 40%.
What will be the new steady state growth rate of output?

(c) Is the rate of growth of output in the new steady state equilibrium different
from that obtained just before attaining the new steady state (after
deviating from the old steady state)? Explain.