Question

2.- You are a monopolist with 15 potential buyers for the two video games you sell, VG1 and VG2. You can produce each of these games at constant marginal cost of $1. There are 3 different types of clients: type A (3 of them), type B (5 of them) and type C (7 of them). The types' willingness to pay for each of the games is given in the following table (each client would buy at most one unit of each of the games): VG1 VG2 Type A 10 15 Type B Type C 14 (a) If you can only set (linear) prices for each of the two games, what prices would you select? (b) Can you do better with two part tariffs? (c) Can you do better by selling ONLY the package with the two games? What would then be the price of the package (bundle) that you would set?

Answer 1

A) VG1 ,

If p=14, then only type c will buy and TR=14 and profit=13,

If p=10, then type c and A will buy and TR=20 and profit=18

If p=9 ,then All will buy and TR=27 and profit=24,

So to maximize profit price of VG1 will be set =9

VG1,

If p=15,then only type A will buy and TR=15 and profit=14

If p=10, then type A and c will buy and TR=20 and profit=18

If p=6 ,then all will buy but TR=18, and profit=15

So to maximize profit , price of vg2 will be set=10

B) IN two part tariff , monopolist set an entry fee and one usage fee.monopolist set usage fee equal to marginal cost and entry fe. Equal to CONSUMER surplus

VG1,

Because here CONSUMERs are different type,so,he can't acquire entire consumer surplus.each CONSUMER have different surplus, the maximum surplus amount from each type of CONSUMER ,he can acquire will be consumer surplus of least type of CONSUMER (B) when p=MC. That surplus will be entry fee.if we charge entry fee more than that, type B CONSUMER will leave the market because then the entire amount he will be paying exceeds his willingness to pay.

P=MC=1

Then, CONSUMER SURPLUS of B=9-1=8

If charge entry fee >8,then the amount type b is paying will be > 9( exceeds his willingness to pay,so he will not buy the vg1)

Best entry fee=8

And usage fee =1

TR=8*3+1*3=27

Profit=24

VG2,

Best entry fee=9

Usage fee=1

Type b won't buy

TR=9*2+1*2=20

Profit=18

So No, two part tariff is not Increasing profit.

C) bundle willing to pay,

Type a=10+15=25

Type b=15

Type c=24

If p=25, only type A will buy and TR=25 and profit=23

If p=24,then tye a and c will buy and TR=,48 and profit=44

If p=15, then all will buy and TR=45 and profit=39

,So to maximize the profit bundle price must be equal to 24

Will it be beneficial,

Without bundling profit=24+18=42

With bundling=44

So yes , selling games in bundles will increase profit.