Question

3. A yoga classroom faces two demand curves. The demand by local residents is Q=100-0.5P, and the demand by nonlocal residents is Q=200-0.5P. The marginal cost of serving either local or nonlocal residents is constant at $100. If the yoga classroom practices third-degree price discrimination, it will charge local and nonlocal residents a price of _____ and _____, respectively.

a. $150; $250

b. $100; $200

c. $250; $350

d. $200; $300.

How many people will they serve if they charge the same for both?

How much profit increase do they have when they switch from uniform pricing distribution?

Answer 1

Demand by local residents is

Q = 100 - 0.5P  

0.5P = 100 - Q  

P = 200 - 2Q

MR = 200 - 4Q

Demand by non local residents is

Q = 200 - 0.5P

0.5P = 200 - Q

P = 400 - 2Q

MR = 400 - 4Q

MC = 100

If yoga classroom practices third degee price discrimination then

MR_L = MR_NL = MC   

MR_L = MC   

200 - 4Q = 100

200 - 100 = 4Q  

100 = 4Q  

Q = 25

P = 200 - 2(25) = 200 - 50 = 150

MR_NL = MC   

400 - 4Q = 100

400 - 100 = 4Q  

300 = 4Q  

Q = 75  

P = 400 - 2(75) = 400 - 150 = 250

Yoga classroom will charge $ 150 to local residents and $ 250 to non local residents

Terefore (a) is correct option

If yoga classroom charges same price to the both type of residents then total demand is given by

Q = 100 - 0.5P + 200 - 0.5P  

Q = 300 - P  

P = 300 - Q  

MR = 300 - 2Q

MC = 100  

MR = MC  

300 - 2Q = 100

300 - 100 = 2Q

200 = 2Q

Q = 100

P = 300 - 100 = 200

Thus yoga classsroom will serve 100 people

Profit = 200100 - 100100

= 2000 - 10000 = 10000

Profit when yoga classroom practices third degree price discrimination  

Profit = 15025 + 25075 - 100(25 +75)  

= 3750 + 18000 - 10000

= 11750

Profit increses by 1750 when yoga classroom practices third degree price discrimination  

Note  MR_L= Marginal revenue for local residents

MR_NL =  Marginal revenue for non local residents