An apartment block has seventy units of accommodation. It is estimated that it is possible to let them all if the rent is $2,000 per month, and for each $100 per month the rent is increased there would be one unit vacant. LG, the manager of the block, finds that a vacant unit costs $100 per month to maintain whereas an occupied one costs $300.
a. If profit from the lettings is measured as revenue minus maintenance costs, find an expression for profit in terms of the number of units let.
b. What rent should LG charge to maximize profit?
c. KA, a contractor, offers to be responsible for the maintenance of the entire block at a rate of $150 per unit, whether the units are occupied or not. Would it be more profitable for LG to employ KA?
2. XL Corp has estimated its demand and cost functions to be as follows:
P = 60 0:2Q
C = 200 + 4Q + 1.2Q 2
where Q is in units, P is in $ and C is in $.
a. Calculate the profit maximizing price and output.
b. Calculate the size of the profit.
c. Calculate the price elasticity of demand at the above price.
d. If there is a $14 tax placed on the good, so that the producer has to pay the government $14 for every unit sold, calculate the new profitmaximizing price and output.
e. What would happen to profit if the firm tried to pass on all the tax to the consumer in the form of a higher price? f. If fixed costs rise by $200 how would this affect the firm’s situation?