Suppose the demand for housing D is given by the function D=100p^-1r^-2 where p is the price of housing and r is the mortgage interest rate. Treat r as exogenous. The supply of housing is given by s=s1 , where S is exogenous.
i) Solve for the equilibrium housing price and then by partially differentiating your reduced form, carry out a comparative static analysis with respect to the mortgage interest rate and the housing supply. Explain (in plain English) why your answers make sense and be sure to depict each change that takes place in a simple (two-dimensional) diagram.
ii) Suppose the demand for housing is changed from above to a general function D=D(p,r) Dp<0, Dr<0 The supply of housing is still the same. Again, conduct a comparative static analysis with respect to the mortgage interest rate and the housing supply.