ISI 2015 sample question - Stumped

[Rajat]

Hi,

I am just not able to get my head round this problem. Can someone please help with this

Suppose a government agency has a monopoly in the provision of internet
connections. The marginal cost of providing internet connections is ½, whereas the
inverse demand function is given by: p = 1 – q. The official charge per connection is
set at 0; thus, the state provides a subsidy of ½ per connection. However, the state can
only provide budgetary support for the supply of 0.4 units, which it raises through
taxes on consumers. Bureaucrats in charge of sanctioning internet connections are in
a position to ask for bribes, and consumers are willing to pay them in order to get
connections. Bureaucrats cannot, however, increase supply beyond 0.4 units.
1)Find the equilibrium bribe rate per connection and the social surplus.
2)Now suppose the government agency is privatized and the market is
deregulated; however, due large fixed costs of entry relative to demand, the
privatized company continues to maintain its monopoly. Find the new
equilibrium price, bribe rate and social surplus, specifying whether
privatization increases or reduces them.
3) Suppose now a technological innovation becomes available to the privatized
monopoly, which reduces its marginal cost of providing an internet
connection to c, 0 < c < ½.Find the range of values of c for which
privatization increases consumers' surplus.

Thanks !

[Anakin Skywalker]

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[Rajat]

Thanks skywalker.

Though the solution is simple, language of the question is really confusing.
part (a) asks us the equilibrium bribe rate which you have shown to be 0.6. But why does the question call it 'bribe'?  It is after all the equilibrium price determined by the market (monopoly market ofcourse)

part (b) asks us to find the equilibrium price AND the bribe rate. Are these two different now? were they not different in the previous question ?

[Anakin Skywalker]

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[L]

For part (a), what I thought was Q can never exceed 0.4 as govt. is not charging anything directly. So, Q=0.4 and P=0. Then, CS= 0.32 which should be equal to bribe/connection.
I don't think bribe should be equal to 0.6 because that would mean CS of 0.6 under demand curve.
 And social surplus (SS) = surplus to bureaucrats + consumer surplus.
Since govt. is charging customers indirectly via taxation, Cost to consumer = .5*.4 =0.2
So, CS = -0.2 (as 0.32 is lost  in bribes)
So, SS = 0.32-.2 = 0.12



For part (b), I differ with you in SS. you have included cost in surplus which shouldn't be there.
So, SS= 1/2 * (0.5+0.25) 0.25 = 0.09375.
And deregulation should not mean zero bribes because after deregulation too, nothing has changed. Same one company but just not under govt. Generally, deregulation leads to competition which removes this side business. So, bribes = CS = 0.03125

For part (c), I agree with your solution.

PS: I am also not sure about my reasoning. Tell me if I am misinterpreting something.

[Anakin Skywalker]

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[L]

Isn't the bribe case similar to two-part tariff, like the example of Disneyland mentioned in Hal Varian.

[onionknight]

Why do you always set consumer surplus= bribe. Since the bribe rate per Internet connection just comes off as an additional cost of say Rs.b per connection,  this would reduce the demand (q=1-p).

Here is my solution to this problem:
In the first case,  the firm has a marginal cost of 0.5 per connection and the government subsidises each connection by the same amount which makes profit=0 irrespective of the quantity produced and so the firm would be ready to supply any quantity. So the cost incurred by the customers would only be 'b'. Thus q=1-b. Now the payoff for the bureaucrats would be (1-b)b which would be maximised at b=0.5 which is unattainable and hence they would settle down for b=0.4 and q=0.6.

Part 2:Now let p be the price charged by the firm, the total cost being borne by the consumer is p+b which means q=1-p-b.  The payoff for the firm is thus (1-q-b)q- 0.5*q. To maximise payoff, the firm would produce (0.5-b)/2. Now the payoff for the bureaucrats is b*(0.5-b)/2 and to maximise this b=0.25 and thus q= 0.125.

[L]

Why I am setting CS=Bribe, for that you just refer to Pg - 476 of Hal Varian. Correct  me If I am wrong.
Then, only I will start to think in your way. Till now, I think that is the way of calculating bribe.

And also, I think there is a typing mistake in your answer, given you are doing it correct. It should be q=0.4 and b=0.6 .

This question is very flexible. Everybody has different explanations.
Also, I was thinking it has been asked bribe rate per connection. then, it should be b/q not just b.

[onionknight]

Yes, it is b=0.6 and q=0.4.

Doesn't quite look wrong to me at first glance but I'll think about it.

[onionknight]

L, your solution would be right if the demand function given in the question was that for a single firm. The demand function here is the market demand function. If you suck the entire surplus of a single consumer he would still be indifferent between buying and not buying the good ( given that he had the same demand function). In this case however, as bureaucrats suck consumers' surplus the market demand would go to 0.

[L]

I didn't understand your comment. Here, market demand function is indeed the demand facing the firm as it is the only one in market.
I am pretty confused now. Both solutions seems right to me but both give different answers.
And how you are taking into account the imposition of taxes on consumers as an indirect way to meet cost by the government.
I think for the first part, this indirect cost should be involved too. In that case my solution will change,
Bribe rate/connection = CS/q = (0.32-0.2)/0.4 = 0.3  ( term 0.2 is the area for 0.5*0.4).

[onionknight]

The two tariff part thing you read from varian works when you are given a single consumer's demands curve,check in the book. Because in that case even after the bureaucrats suck the representative consumer's consumer surplus entirely he'll still be indifferent between consuming and not consuming. It's the market demand curve.

The fact that the government is imposing a tax only changes the social surplus and has no effect on the bribe rate.

[L]

Check the image:

It is consumers' surplus. Admission charge = CS/ number of people.

[art]

im thinking that we shld do MR=MC....why isnt nobody doing this? and how can CS be 0.32 i mean at q=.4 and p= .6 the area comes to be .08  can someone explain with a graph please