A firm called Shanghai Housing Limited has won a tender to build housing units within

the Durham city council. As part of its initial planning, it found out that the demand and

supply functions for houses in Durham are given by the following:

Ps = + Qs and Qd = Pd

a) Represent the above functions on a suitable graph, properly labeling all the axes and

curves.

b) Find the equilibrium values of quantity and price.

c) In order to increase housing units, Durham local council is thinking to offer a

subsidy of k per housing unit. Discuss, using post-subsidy expressions, the

possible effects on equilibrium house prices and quantities if this decision is

implemented.

d) Write expressions for the price elasticities of demand and supply of housing after

the granting of the subsidy.

e) Write appropriate expression showing the projected total expenditure of Durham

county council that is related to the subsidy.

Information available to Shanghai Housing Limited also indicated that the total variable

cost for such a project is given by:

TVC(Q) = Q2 + Q

Where Q is quantity of housing units produced and and are positive constants. You

also know that the total costs is approximated to be if no housing units are produced.

f (i) Using appropriate equations, write the estimated housing profit function for

this firm.

f (ii) Using your information from f(i) or otherwise, work out an expression for

the number of housing quantity that will maximize profit.