Question

In: Economics

a monopolist knows that there are 2 types of consumers, "high demand" and "low demand" types....

a monopolist knows that there are 2 types of consumers, "high demand" and "low demand" types. Inverse demand for low is p=150-qL and p=200-qH . 70% of consumers are the L type. MC =0.

a) find the optinal price if the firm can only set one price.

b) explain how a firm can set a fee for purchasing any amount and why it is better than single price strategy.

Solutions

Expert Solution

Step 1
p=150-qL , p=200-qH , MC =0

The type L is 70% of consumers
Complete revenue (TRL) = 150qL-qL2
Complete revenue (TRH ) = 200qH - qH2
Marginal Revenue (MRL) = 150 - 2qL
Marginal Revenue (MRH) = 200 - 2qH

Step 2
For a monopolist:
1. MRL =MC 2. MRH =MC
150 - 2qL =0 200 - 2qL =0
2qL = 150   - 2qL = - 200
qL = 150/2 qL = - 200/-2
qL =75 qL = 100
pL = 150-qL   pL = 200-qL
pL = 150 - 75 pL = 200-100
pL = 75 pL = 100


Step 3
Optimal price if only one price can be set by the firm: , pL = 75
As it is a cheaper price and all buyers are going to purchase the stuff.

Step 4

A fee for buying any amount will be set by the company:
70% of customers are in low demand,
qL = 0.7X75 , qL = 52.5 units

Price will be:
PL = 150 - 52.5 = $97.5

30% of customers in high demand are
qH = 0.3X100 , qH = 30 units

The price is going to be:
PH = 200 - 30 = $170

Thus, due to the demand from the customer, the business can charge rates.It is safer than a single pricing approach so the business will gain greater revenues by charging buyers with high demand at a higher price.

Rahul Sunny answered 2 years ago
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