# How to Determine Third-Degree Price Discrimination in Managerial Economics

In order to determine the profit-maximizing price and quantity for each group of customers by using third-degree price discrimination, you must satisfy the following condition:

where *MR*_{A} is group A’s marginal revenue for the last unit it buys, *MR*_{B} is group B’s marginal revenue for the last unit it buys, and *MC* is marginal cost for the last unit you produce.

Assume that the following equations describe the demand for your firm’s product for two different groups of customers. Group A’s demand is

where *P*_{A} is the price in dollars charged to group A customers, and *q*_{A} is the quantity sold to group A customers. Group B’s demand is

where *P*_{B} is the price in dollars charged to group B customers, and *q*_{B} is the quantity sold to group B customers.

Your firm’s total cost and marginal cost equations are

where *TC* is your total cost in dollars, *MC* is marginal cost in dollars, and *q* is the total quantity of the good your firm produces.

Using this information and the following steps, you can determine the price to charge each group of consumers, how much to sell each group of consumers, and how much to produce:

Determine the marginal revenue for group A customers.

First, multiply the demand equation by

*q*_{A}to determine total revenue, and then take the derivative of total revenue with respect to*q*_{A}to determine marginal revenue.Determine the marginal revenue for group B customers.

First, determine total revenue by multiplying

*P*_{B}by*q*_{B}, and then take the derivative of total revenue with respect to*q*_{B}to determine marginal revenue.Set

*MR*=_{A}*MC*.Substitute

*q*+_{A}*q*for_{B}*q*.The total quantity of output you produce and sell,

*q*, is sold to customers in either group A or group B.Solve the equation in Step 4 for

*q*._{B}Set

*MR*equal to_{A}*MR*._{B}Substitute

*q*= 950 – 5_{B}*q*in the equation in Step 6._{A}Solve for

*q*._{A}Substitute

*q*= 150 in group A’s demand equation to determine the price,_{A}*P*, to charge customers in group A._{A}Substitute

*q*= 150 in the equation from Step 5 to determine_{A}*q*._{B}Substitute

*q*= 200 in group B’s demand equation to determine the price,_{B}*P*, to charge customers in group B._{B}Determine the total quantity of output that your firm produces.

Your firm produces 350 units of the good. It sells 150 units to customers in group A at a price of $70 per unit and 200 units to customers in group B at a price of $60 per unit.