Question

Show all your calculations. Answers without explanations or calculations will receive a mark of zero. (This question is worth 20 marks in total.)

Telstra is a monopolist. Suppose it operates at the market with demand P = 5 – Q and has the following cost structure: MC=AC = 1.

Draw the market demand curve and the marginal cost curve on the graph with Q on X-axis. (Include a large and accurate graph).

d. Suppose that now Telstra can identify each consumer’s willingness to pay and thus decides to perfectly price discriminate. What will be Telstra’s output and profits? Calculate the new consumer surplus, producer surplus, and deadweight loss. Show your answer on the graph.

In what follows Telstra once again can only charge a single price per unit of service but now faces two types of customers: residential customers with the demand curve given by the following: P = 5 – Q. Further, business owners whose demand is given by P = 7 – Q/2. There is an equal number of consumers of each type.

e. Suppose Telstra CAN identify whether the customer is a residential or business customer and can charge different prices to each type. What are the optimal prices and quantities for these groups of consumers? Illustrate your answer on a separate graph, showing consumer surplus, producer surplus, and deadweight loss.

f. Calculate the point price elasticity of demand for both types of customers at the price and quantity you identified in part (e) of the question.

g. Now suppose Telstra CANNOT tell whether the customer is a residential or business. Calculate the aggregate demand by adding up residential and business demands horizontally. Find the optimal price, output, and profits for Telstra if it can only charge a single price for everybody. Compare this outcome with your answers to part (e).

Answer 1

Market demand for the monopolist is given by P = 5 - Q. This monopolist has a fixed MC for each additional unit of output it produces, given by MC = AC = 1.

The graph for the market demand and marginal cost curve is given below:

Part d) Since Telstra perfectly price discriminates its customers, it charges each customer his/her reservation price, which is the maximum price a customer is willing to pay for a given quantity. Normally, a monopolist sells until the point MR = MC. However, in this case, it sells until the point its MC is equal to the reservation price/ the demand curve of the customer.

Consider the table below for an example of the reservation price:

Quantity	Reservation Price	Marginal Cost
1	4 ( = 5-1)	1
2	3	1
3	2	1

Thus, equating marginal cost to the demand curve, we get Q= 4.

Total revenue(refer to the shaded triangle in the graph below) = 1/2x4x4 = 8

The total cost of producing 4 units of output = 4.1 = 4.

Thus, Telstra's profit = 8 - 4 = 4.

For the consumer and producer surplus and deadweight loss, look at the graph below:

Since the monopolist extracts the maximum price each customer is willing to pay, it means it extracts the entire consumer surplus and converts it to producer surplus. Thus, the shaded triangle in the graph above is the new producer surplus. It can be calculated using the formula for the area of a triangle.

Thus, Consumer Surplus = 0

Producer Surplus = 1/2 x 4 x 4 = 8

Deadweight loss = 0. There is no inefficiency arising from first-degree price discrimination.

Part e) This is a case of third-degree price discrimination. Refer to the answer below for the calculation of optimal price and quantity for residential and business customers:

For calculation of consumer surplus, producer surplus and deadweight loss at this price - quantity combination, refer to the answer below:

Part f). Point price elasticity for the residential and business customers is given by:

Residential : Elasticity = - (dQ/dP)x(P/Q) = -1 x (3/2) = -1.5

Business: Elasticity = -2 x (4/6) = -1.33

Clearly, elasticity for business customers is less elastic compared to residential customers, so they are charged a higher price.

Part g). Since Telstra can no longer distinguish between its customers, it again charges a single price from all of them. The aggregate demand curve is derived by summing the two demand curves horizontally, and then MR = MC is used to arrive at the price to be charged. Refer to the image below for the calculation: