# Numerical Question on a subsidized monopoly

Suppose a government agency has a monopoly in the provision of internet connections. The marginal cost of providing internet connections is $$\frac12$$, 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 $$\frac12$$ 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.

(a) Find the equilibrium bribe rate per connection and the social surplus.

(b) 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.

(c) Suppose now a technological innovation becomes available to the privatized monopoly, which reduces its marginal cost of providing an internet connection to $$c$$, $$0 < c < \frac12$$. Find the range of values of $$c$$ for which privatization increases consumer surplus.

I understand that the consumers will be willing to trade away all the consumer surplus as bribe to receive the connection. But each consumer has a different willingness to pay as demonstrated by their demand curve or MB. How do I find a single equilibrium bribe rate for the problem? Should I just take the $$Total \ Benefits \ = trapezoid \ area = 0.4\frac{1 + (1-0.4)}2$$. And divide this area with total connection which is $$0.4$$ and thus get the per connection average bribe.

Also total taxes = total subsidy, and also consumer surplus will be just traded away as bribe. So isn't the social surplus the same overall all the time?

• This looks like a problem set. I'm sure you can calculate the points at which the Marginal revenue: $MR=1-2q$ equals the marginal cost, to solve for the monopoly equilibrium, as well as the price of the bribe so that 0.4 units are demanded to find $a)$. You should get a smaller social surplus in $b$ than in $a$, and you should find in $c$ that for $c\in(0,\bar c)$ privatization increases consumer surplus, for some threshold $\bar c$, and for $c\in(\bar c, 1/2)$ consumer surplus decreases. If your solution has all these properties, you'll know you did it right. – Regio Apr 27 '19 at 21:11