Question

Kenny McCormick manages a 100-unit apartment building and knows from experience that all units will be occupied if rent is $900 per month. McCormick also knows that, on average, one additional unit will go unoccupied for each $10 increase in the monthly rental rate. A. Estimate the apartment rental demand curve assuming that it is linear and that price is expressed as a function of output. B. Calculate the revenue-maximizing apartment rental rate. How much are these maximum revenues

Answer 1

A. Estimate the apartment rental demand curve assuming that it is linear and that price is expressed as a function of output.

the demand curve's slope = -10 / 1 = -10

demand curve = a - 10b

since all 100 units will be rented when p = $900

900 = a - 10(100)

900 = a - 1,000

1,900 = a

demand curve = 1,900 - 10b

B. Calculate the revenue-maximizing apartment rental rate. How much are these maximum revenues

we must first fin total revenue and then find hte derivative

total revenue = p x a

total revenue = (1,900 - 10a) x a

total revenue = 1,900a - 10a²

revenue maximizing quantity' = 1,900 - 20a

20a = 1,900

a = 95 apartments rented

price = 1,900 - (95 x 10) = $950

total revenue = $950 x 95 = $90,250