Question

1. Like the monopolist, you are a price-maker. But suppose you can practice access pricing. Demand is P=50-0.05Q and you can produce each unit of output for $30 a unit. That is, AC=MC=$30. To make the story right each potential customer has this demand of P=50-0.05Q. You need to draw a graph to answer some parts below.
   1. What first price or access price should you charge?

   2. What is the 2^ndprice or price per unit of output that you should charge?
   3. How much output will each customer buy?

   4. What are your profits from each customer?

Answer 1

First we draw the curve in this situation

We calculate the price at which demand is zero.

P=50-0.05Q

Put Q=0

P=50-0.05*0=$50

Now let us calculate, Q at P=$30

30=50-0.05Q

Q=(50-30)/0.05=400

With the help of above information, we can make the following graph.

In this graph, demand curve is shown by blue line and we have a horizontal line at P=$30.

a)

In this type of price discrimination, Price per unit is charged such that P=MC

P=MC=$30

Access fee = Consumer surplus at P(=MC)

Consumer surplus at P=$30 is

CS=1/2*(50-30)*(400-0)=$4000

Access fee should be $4000

b)

Second price is equal to marginal cost i.e. $30 per unit.

c)

We have already calculated the custimer's demand at P=$30. It is 400 units.

Customer will buy 400 units.

d)

Total revenue per customer=AC*output=30*400=$12000

Total cost per customer=Access fee+Sale revenue=Access fee+P*Q=4000+30*400=$16000

Total profit per customer =Total revenue-Total cost=16000-12000=$4000