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7. A monopolist has cost function  =  + 2 and the regulator is willing to allow the firm to use a two-part tariff per consumer  =  +  to cover total costs. Total demand is  = 102 −  and there are 100 identical consumers. Up to how much is willing to pay each indidual consumer to have the right to consume the good at marginal cost? What is the optimal tariff or tariff that would maximize social welfare (fixed part and marginal price) ?

Sagot :

batolisis

Answer: hello your question is poorly written  below is the complete

A monopolist has cost function C = F + 2Q and the regulator is willing to allow the firm to use a  two-part tariff per consumer equal to T = A + pq to cover total costs. Total demand is Q = 102 − p and  there are 100 identical consumers. What is the optimal tariff or tariff that would maximize social welfare  (fixed part and marginal price)?

answer :  Fixed part = $5000 per customer = $500,000

               marginal price = $2

Explanation:

Marginal cost of monopolist = dc / dq = 2

Q = quantity of the concerned good/service.

p = price of concerned good/service

Based on profit maximizing condition of the monopoly firm under the two-part tariff system ; output of concerned goods/services = MC = price of concerned goods/service

P = MC

102 - Q = 2   ∴ Q = 100

back to the Total demand function ( p = 102-Q )

p = 102 - Q

p = 2

when Q = 0

p = 102 - Q = 102

hence; Total consumer surplus = 0.5 * ( 102 - 2 ) * ( 100-0 ) = $5000 i.e. fee charged by monopolist per customer

marginal / socially optimal price charged = $2

Total Fixed rate/part that the monopolist will charge from 100 customers

= (100*5000) = $500,000

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