Question

Third degree price discrimination

A software company is selling accounting software in both domestic and foreign markets.

Because of differences in the legal framework, an accounting program purchased in one market cannot be used in the other market (hence price discrimination is possible).

The inverse demand functions in the two markets are specified as follows:

P_D= 6250 - 25Q_D

P_F= 4000 - 10Q_F

Since the firm is obliged to train the staff of the purchasing firm to work with the software, it has to employ a trainer and an IT specialist every time it sells an extra unit. They each earn 1500 Euro per training. It also pays 4000 Euro to each of its 10 software engineers (regardless of their productivity or how much it sells).  

The cost function ofthe firm is thus:

C= 10?4000 + (1500 + 1500)(QD+QF) = 40000 + 3000(QD+QF)

Since the price discrimination is possible, the firm would like to sell the software at different prices for two markets. How many software packages will the firm sell on the domestic market (QD)?
At what price will it sell (PD)?  
How many packages will be sold on the foreign market (QF)?  
At what price (PF)?  
What is the profit of the firm in this case?

Answer 1

When monopolist uses third degree price discrimination, it will charge two different prices from two different consumer groups. Use the MR = MC rule where for the given question, MC = 3000

PD= 6250 - 25QD PF= 4000 - 10QF

TRD = 6250QD - 25QD^2 TRF = 4000QF - 10QF^2

MRD = dTR/dQD = 6250 - 50QD MRF = 4000 - 20QF

Profit maximization results

MR = MC

6250 - 50QD = 3000 and   4000 - 20QF = 3000

QD = 3250/50 = 65 and QF = 1000/20 = 50

Price in domestic market PD = 6250 - 25*65 = $4625

Price in foriegn market PF = 4000 - 10*50 = $3500

Total profit = TRD + TRF - C = PDQD + PFQF - C = 65*4625 + 50*3500 - 40000 - 3000*(65 + 50) = 90625.