<p>You probably want to assume that every consumer pays the same bribe. Also, the social surplus depends on the quantity consumed, so it might (spoiler alert: it will) change when the internet is privatized, and when the marginal cost changes.</p>

CC BY-SA 4.0
2019-04-26T20:05:19.253Z
Thanks for your answer. Can you solve them and atleast give me the answer key if not the solution, so I can compare my answers and ask more if they don't corroborate.
metrics24
CC BY-SA 4.0
2019-04-27T21:11:14.517Z
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
CC BY-SA 4.0
2019-04-25T22:05:22.663Z
2019-04-25T22:05:22.663Z
Regio
<p>Suppose a government agency has a monopoly in the provision of internet connections.
The marginal cost of providing internet connections is <span class="math-container">$ \frac12$</span>, whereas the inverse demand
function is given by: <span class="math-container">$p = 1 - q $</span>. The official charge per connection is set at 0; thus,
the state provides a subsidy of <span class="math-container">$\frac12
$</span>
per connection. However, the state can only provide budgetary support for the supply of <span class="math-container">$0.4$</span> units, which it raises through taxes on consumers.</p>

<p>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 <span class="math-container">$0.4$</span> units.</p>

<p>(a) Find the equilibrium bribe rate per connection and the social surplus.</p>

<p>(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.</p>

<p>(c) Suppose now a technological innovation becomes available to the privatized monopoly,
which reduces its marginal cost of providing an internet connection to <span class="math-container">$c$</span>, <span class="math-container">$0 &lt; c &lt; \frac12$</span>.
Find the range of values of <span class="math-container">$c$</span> for which privatization increases consumer surplus.</p>

<p>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 <span class="math-container">$Total \ Benefits \ = trapezoid \ area = 0.4\frac{1 + (1-0.4)}2 $</span>. And divide this area with total connection which is <span class="math-container">$0.4$</span> and thus get the per connection average bribe.</p>

<p>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?</p>

<microeconomics><monopoly><social-welfare><consumer-surplus>
Numerical Question on a subsidized monopoly
metrics24
# Numerical Question on a subsidized monopoly

(Asked by: username_0 on 2019-04-24)

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?

**Tags:** microeconomics, monopoly, social-welfare, consumer-surplus


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## 1 answers

### Answer by username_1 on 2019-04-25. Score: 1

You probably want to assume that every consumer pays the same bribe. Also, the social surplus depends on the quantity consumed, so it might (spoiler alert: it will) change when the internet is privatized, and when the marginal cost changes.

> **Comments:**
> **username_0**: Thanks for your answer. Can you solve them and atleast give me the answer key if not the solution, so I can compare my answers and ask more if they don't corroborate.  
> **username_1**: 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.  

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