Suppose there are two types of customers for a cell phone service: undergraduate

Question

Suppose there are two types of customers for a cell phone service: undergraduates (U) and grad Students (G). The aggregate (inverse) demand curve for undergraduates is PU = 100 - 0.25QU and The aggregate (inverse) demand curve for The graduate students is PG = 50 - QG. The firm providing The cell phone service is a monopolist with a cost function characterized by C(Q) = 4Q + 10. Suppose The firm is restricted to set a single price for both types of customers (i.e., no price discrimination). What price does The firm set? How much profit does The firm collect? How much consumer surplus is generated at The price identified in (a)? Suppose The firm sets a price of $48 for a quantity smaller or equal than 200 minutes and a price of $46 for a quantity beyond The 200th minute. In this situation, what quantity should undergraduates choose? And what quantity should graduate students choose? What consumer surplus will each customer type enjoy at The prices set in (c)? How much profit does The firm collect with The prices set in (c)? (f) Why would a firm choose a second-degree price discrimination strategy rather than a first-degree price discrimination strategy? (You only need to provide one reason)

Explanation / Answer

(a) Pu= 100 0.25QU

TRu=100Qu-0.25Qu2                                      (TR=P*Q)

MRu=100-0.5Qu

PG = 50 – QG

TRg=50Qg-Qg2  

MRg=50-2Qg                                                      (TR=P*Q)

C(Q) = 4(Qu+Qg) + 10

MCu=4

MCg=4

Equiibrium and profit max condition for the monopolist will be MR=MC

MRu=MCu

100-0.5Qu=4

Qu=96/0.5

=192

MRg=MCg

50-2Qg=4

2Qg=46

Qg=23

Now Pu= 100 0.25QU

Pu=100-0.25*192

Pu=52

PG = 50 – QG

Pg=50-23

=27

If the monopolist need to set same prices of both the products, the price set will be 52, being the monopolist the firm will charge higher price for both the products.

Profit(u)=52*192-(4*192+10)=9206

Profit(g)= 52*23-(4*23+10)=1094, for price 52

Profit(g)= =27*23-(4*23+10)=519, for price 27

Consumer Surplus(u)=1/2*48*192=4608 (for price 52)

Consumer Surplus (g)=1/2*(-2)*23=-23 the negative consumer surplus is due to setting up of price of graduate students higher than the equilibrium price if the price set is 27 than the consumer surplus would have been =1/2*23*23=264.5

(d)

If the firm sets a price of $48 for 200 and $46 beyond 200

Then the CS=1/2*52*200=5200 (price of $48 for 200) for undergraduates

The consumer surplus would be greater in quantity beyond 200 they should chose more than 200 minutes.

CS=1/2*2*200=200, for graduate students if the initial equilibrium price chosen is 52. (price of $48 for 200)

The consumer surplus would be greater in quantity beyond 200 for graduates too

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