ISI ME II 2012

[neha.]

has anyone done question 14? what answer are u getting???

[anon_econ]

am getting 14/15 and 1/6

[ritu]

@vasudha
i got for this question that monopolist will produce total output of 3/2 of which he sells 2/3  in home and 5/6 in foreign....total output is decided by equating mr of foreign with mc.....and domestic output is decided by equating mr of home and foreign....m confused regarding quota part though...

[neha.]

Hi vasudha,, thanks for replying,,, but can u explain hw did u get these?

[deepak]

Ritu's answer is correct. However, the question explicitly mentions he can't sell more than 1/6 to a foreign country. But his optimal choice indicates he'd like to sell more abroad (intuitively, you can see this making sense as he can charge more for exports). So keeping in mind he wants to sell as much as possible abroad as long as he sells less than 5/6 abroad (which is his point of max profits) we can say that he will necessarily export 1/6 of the good to the foreign country. This leaves us with just optimising quantity sold domestically, taking the exports to be a fixed value of 1/6. If you proceed with this, you will get Vasudha's answer

[neha.]

thanks deepak,,, but i still could nt get it,,, u mean we shud equate domestic MR with MC?

[deepak]

The profit function is given by Domestic Qty * Domestic price + Export Qty * Export price - Cost (Domestic + Export).
Now, as mentioned in the previous argument, the profit maximizing level of export would by the entire allocation of 1/6. Export Price is 3. Taking domestic qty sold as qh, profit function is
Profit = (5 - (3/2)qh) * qh + 3*1/6 - (qh + 1/6)^2
Setting the first order to 0 would give you qh = 14/15

[neha]

Thanks Deepak :)

and what answers are u getting for Q10 of the same paper?

[ritu]

so for part without quota answer is 2/3 in home and 5/6 foreign and with quota ...14/15 at home and 1/6 foreign??????????

pls pls confirm....

[anon_econ]

Yes ritu :)

[deepak]

Neha,

For question 10 part 1, equating their marginal rates of substitution yields x1 = x2 ie contract curve is given by the straight line joining the origins.

Part 2,
a) If you equate profit P = 80 = (10-x/10) * x - 4*x and solve the quadratic equation, you will get the answers x = 40 or x = 20. In the question they specifically mention 'max' revenue. You will find that revenue when x = 40 is greater than when x = 20

b) Max profit for the given demand function and marginal cost is 90. Hence a profit of 100 is impossible to achieve

c) Under the new marginal cost of 8, the maximum achievable profit would be Rs 10. So he can't make the original profit of 80 in this case. (not entirely sure about my calculations on the part c. Too lazy to double check, sorry :P)

Does this look right to you?

[ritu]

A monopolist has cost function c(y) = y so that its marginal cost is
constant at Re. 1 per unit. It faces the following demand curve
D(p) =100/p,,.p<=20
         0.p>20
Find the profit maximizing level of output if the government imposes a
per unit tax of Re. 1 per unit, and also the dead-weight loss from the
tax....

MY ANSWER
here revenue is always 100 so he wud mininmise cost for any output...."WITHOUT TAX "he wud charge a price of 20,sell 5 units at a cost of 5 and take away 95 as profit but what will happen if mc rises to 2 coz of tax?????
will he still charge a price of 20 ,sell 5 units but profit now falls to 90 as he the cost of 5 units is now 10??????
regarding dwt loss....consumers are as well off as before coz price cant rise beyond 20  but monopolist''s profits fall so is dwt loss=rs 5 which is the amount by which his profits fall....???????????????
pls correct me wherever m wrong:)

[ritu]

these 5 rs will be collected by govt....so as a whole economy is as well off but individually monopolist is worse off????

[anon_econ]

yup. no deadweight loss and the monopolist's profit falls.

[deepak]

Hi Vasudha and Ritu,

This is about the question 6 in the 2012 paper.

Like Ritu mentions, his revenue is a constant 100. Since a monopolist is only concerned about profits, he would want to minimise his cost ie, produce as little as possible while still generating +ve revenue. Hence, he produces only 1 good. So Profit = 100-1 = 99 (his maximum profit, assuming discrete goods).

However, when a tax is levied, the price is marked up with the tax ie y = 100/p' or p' = 100/y and we can write p' = p+1. So py + y = 100, or py = 100-y is the after tax revenue.

Profit = Revenue - cost = (100-y) - y = 100 - 2y. This is maximum when y = 1. Max profit = 98.
Price before tax = 99. After tax price = 100. Tax revenue for the government = 1.
Consumer surplus is unchanged (=0. Since only 1 good is sold, it is sold by the monopolist at the buyers' reservation price).
Producer surplus is reduced by 1 (here I take profit to indicate producer surplus as no fixed cost is mentioned)

So isn't the NET deadweight loss = 1 here? The consumers are no worse off than earlier, but the producer is worse off by Rs.1 so the deadweight loss is 1 right? Since the price paid by the consumer is different from the price received by the producer, the solution is not pareto optimal (not in equilibrium) and must involve a deadweight tax, right? Or am I missing something?

[Mr. Nobody]

CONTENTS DELETED

The author has deleted this message.

[lovekesh]

Deepak
It's not deadweight loss. It's a mere distribution of money from producer to government.

[deepak]

Lovekesh, in the computation of deadweight loss, do we not consider only the producer and the consumer? Is the government's fortune also to be included in the boundary to compute the deadweight loss? http://en.wikipedia.org/wiki/Deadweight_loss
If you look at that, it describes what we face - there is a portion of the producer surplus (in our case) that is being lost out because we're not in market equilibrium. It necessarily means that the market is not 100% efficient and that this is a deadweight loss, right? I am merely postulating here and don't know for sure.

[deepak]

Ram, yes indeed! Oversight on my part. Apologies. Thanks for the spot :)

[lovekesh]

"The specific tax on roses creates an 11¢ per stem
wedge between the price customers pay, 32¢, and the
price producers receive, 21¢. Tax revenue is T = τQ =
$127.6 million per year. The deadweight loss to society is
C + E = +4.95 million per year."

The above statement is from perloff. Here it clearly says DWL is 4.95 which is less than the tax paid which is 127 million dollars. So, as a thumb rule which i follow, see if there's any loss in production or extra item is being produced at a higher marginal cost while people don't value that is, their marginal benefits is lower than what it cost to produce them. For example, gifts. If someone bought me samsung pad which cost them around 30K, for me it's value is nothing more than 20K. So, that is a social DWL. In that question, a TAX changes nothing. People are still buying what they were buying before. It's simply producers are hurting but that portion is also going to someone. In that case, then DWL is zero. DWL is calculated by change in welfare. Welfare of every agent involved is considered in calculating that. Generally taxation causes DWL, but that's because it intereferes with market and people buy less goods and some people get left who were willing to pay money at competitive price but couldn't do so.