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 (TR_H ) = 200q_H - q_H²
Marginal Revenue (MR_L) = 150 - 2q_L
Marginal Revenue (MR_H) = 200 - 2q_H

Step 2
For a monopolist:
1. MR_L =MC 2. MR_H =MC
150 - 2q_L =0 200 - 2q_L =0
2q_L = 150 - 2q_L = - 200
q_L = 150/2 q_L = - 200/-2
q_L =75 q_L = 100
p_L = 150-q_L p_L = 200-q_L
p_L = 150 - 75 p_L = 200-100
p_L = 75 p_L = 100

Step 3
Optimal price if only one price can be set by the firm: , p_L = 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,
q_L = 0.7X75 , q_L = 52.5 units

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

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

The price is going to be:
P_H = 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 1 year ago

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