Question

3. There are two individuals looking to rent apartments in a neighborhood consumer H is willing to pay $5,000 as monthly rent and consumer L is only willing to pay $3,000 monthly rent. The valuation of the rental for each consumer is given below: Consumer Value of Apartment to Consumer L $3,000 $5,000 н The marginal cost of providing an apartment for rent is $1,000 for each apartment, MC $1,000 Suppose, there is a perfectly competitive rental market in this neighborhood. a) What will the monthly rent be? b) Who will rent at this price? c) What is the consumer surplus? Producer Surplus? Total Surplus?

Answer 1

Solution:

a) Under perfect competition, the price charged by the sellers equals the marginal cost of providing a good or service. In the question, wee are given the marginal cost as $1000 per apartment, thus, monthly rent will be $1,000 for each apartment.

b) The question talks about two consumers only. Notice that the valuation for apartment for both the individuals is higher than the price/rent they face (3000 > 1000 and 5000 > 1000). Since, the valuation from the apartment is higher that the cost they incur to rent the apartment, both, L and H, will rent the apartment at this price.

c) Consumer surplus is the surplus valuation consumers receive over the price they pay. Total consumer surplus is the sum of all individual consumers' surplus.

So, consumer surplus = surplus received by L + surplus received by H

Surplus received by L = 3000 - 1000 = 2000

Surplus received by H = 5000 - 1000 = 4000

Total consumer surplus = 2000 + 4000 = $6,000

Producer surplus is the extra surplus/gain producers receive over the marginal cost (that is, price - marginal cost). Since, under perfect competition, price charged equals the marginal cost, producer surplus equals 0.

Total surplus is simply aggregation of producer and consumer surplus. So,

Total surplus = consumer surplus + producer surplus

Total surplus = 6000 + 0 = $6,000 (or equal to consumer surplus only here, as producer surplus is 0).