ISI PEB (Economics), 2014 ANSWERS 1 TO 5..

[dhruv]

@Rob

For constraints you have demand function for both student and non-student and an additional capacity constraint. You have to carry out optimization such that MR for each market is equal to MC. Also, you can substitute q1 = 150 - q2, and be able to get profits in terms of q2. Through usual first order conditions you can solve for q2 that maximizes profit, and then you will be able to calculate both p1 and p2, all subjected to the capacity constraint.

[Rob]

thanks dhruv and can u explain question 6th as wel ?

[dhruv]

@Rob

I have explained 6(a) in this post. Do you want to know 6(b)?

[Rob]

Yes i just want to noe wt the answers u r getting in  part b specially the 2nd part of 6 (b)

[dhruv]

I got no. of firms = 18. Each producing 5 units of output. I used the fact that when patent expires, firm's monopoly disappears and new firms will enter the market driving the profits to zero.

[Rob]

plzz elaborate the steps how do u reach to this ans?

[dhruv]

Put MC = price and profits = 0, you will get two equations in two unknown.

[Rob]

i tried it m i doin rt?
100 -nq =2 n^2 q
and 2nd  ( 100-nq)nq- 2 n^2 q* nq =0
m i rt?

[dhruv]

You are optimizing for a firm, therefore, for MC, 'n' wouldn't enter the equation. Only in inverse demand function while calculating price you will consider output of the industry. Also, while calculating profits, it should be (100-nq)q, and similarly in other expressions.

[Rob]

thanks dhruv :)

[Rob]

hllo  dhruv
hav u done the isi 2015 me II paper?

[dhruv]

No, I solved previous sample papers, I was leaving it for last.

[Rob]

hav u solvd this? if yess  plz share ur solution


Consider an economy where the agents live for only two periods and
where there is only one good. The life-time utility of an agent is given
by U = u(c) + v(d), where u and v are the first and second period
utilities, c and d are the first and second period consumptions and 
is the discount factor.  lies between 0 and 1. Assume that both u
and v are strictly increasing and concave functions. In the first period,
income is w and in the second period, income is zero. The interest rate
on savings carried from period 1 to period 2 is r. There is a government
that taxes first period income. A proportion  of income is taken away
by the government as taxes. This is then returned in the second period
to the agent as a lump sum transfer T. The government’s budget is
balanced i.e., T = w. Set up the agent’s optimization problem and
write the first order condition assuming an interior solution. For given
values of r, , w, show that increasing T will reduce consumer utility
if the interest rate is strictly positive.  

[raju]

Zen, could u explain how did u get c(q)= 5q in question no-4(a)

Hi ,

Answer to the second ques woud be a=b=10 , as these are satiation preferences. Also intuitively utitlity will be 0 at this point and everywhere else it will be negative.

Answer to its second part will be the same, bcoz these are satiated preferences.

Please correct me if I am wrong

[onionknight]

Can't be the same since the consumer can't afford this bundle with an income of 10 units

Onion ,1st is correct ??

N you r right, I read it as the income is down by 10. Then it will be 5,5

[onionknight]

Yes.

Hey Dhruv,

In ques 6, When the govt is providing 1 to 1 subsidy, it means the slope of the budget line will halve and in the second case it will be shifted outward by 250. N if we draw the we will notice that all the consumption bundle when 1 to 1 subsidy is provided lied under the new budget line. which means the second policy is better.

[dhruv]

Lal family's budget constraint will be,

C + H = M

where, H is housing expenditure, C is other expenditure and M is income.

If government provides one-to-one subsidy on housing expenditure, that implies

C + H = M + H
Hence, C = M

For, new policy their budget constraint will be,

C + H = M + 250