A monopolist firm serves 6 consumers. Each of the consumers only buy one unit of
ID: 1167865 • Letter: A
Question
A monopolist firm serves 6 consumers. Each of the consumers only buy one unit of the good. Two consumers buy one unit if the price is lower or equal than $100 and the other four consumers buy one unit if the price is lower or equal than $10. The firm’s cost function is C(Q) = 5Q.
(a) Suppose the firm is restricted to set a single price for all consumers (i.e., no price discrimination). What price does the firm set? How much profit does the firm collect?
(b) How much consumer surplus is generated at the prices identified in (a)?
(c) Suppose the firm is able to set a personalized price for each consumer (i.e., first-degree price discrimination). What prices does the firm set? How much profit does the firm collect?
(d) How much consumer surplus is generated at the prices identified in (c)?
Explanation / Answer
First of all remember one thing, firm always work for maximisation of the profit, So here also it will try to earn maximum profit as much as it can.
Our Cost function is C(Q) = 5Q i.e total cost earned by the firm is five times of the quantity produced (5 x Quantity)
a) In this case firm will fix the price at $100.
Reason: it has two customers which will buy its product at this price thus total revenue will be $ 200 whereas Cost will C(2)= 5(2)= $10 =, thus earning a profit of $190. Yes it will loose 4 customer in this process but it wont mind as it is earning maximum profit while charging $100 and can easily cover the loss of those 4 customers from the profit earned.
b) Consumer surplus is the difference in amount customer are willing to pay and amount they actually paid.
thus in this case it will be zero , $100(willing to pay) - $100(actually paid).
c) If there can be a price discrimination possible then it will $100 n $10 respectively.
thus Total Cost will C= 5(6) = $30 and Total Revenue will be ($100 x 2) + ( $10 x 4) = $ 240
earning profit of $ 210 i.e Profit = TR - TC.
d) Again the consumer surplus will be zero firm is charging d same amount which consumer is willing to pay, thus there is no difference.