Suppose that in the City of Ottawa, the demand for new houses is given by Qd = D(P,i) = 1000-5P -10i (1) and the supply by Qs = S(P,u) = 500 + 4P + 5u, (2)
where P is the price of houses, i the nominal interest rate set by the Bank of Canada, and u the unemployment rate in the City of Ottawa.
(a) Plot the supply and demand curves on a plot with "Quantity of houses" on the horizontal axis, and "Price of houses" on the vertical axis.
(b) Solve for the equilibrium price P∗ and equilibrium quantity Q∗ in terms of i and u, and also show the location of this equilibrium on your plot.
(c) What is the value of the vertical intercept of the Qd line? What is the value of the vertical intercept of the Qs line?
(d)For each of the variables P,u, explain whether they cause movement along the Qs curve, or a shift in the Qs curve.
(e) In terms of your plot, what does the partial derivative ∂D(P,i) ∂P de- scribe? What about ∂D(P,i) ∂i ?
(f) Now draw a new plot with "Quantity of houses" on the horizontal axis, and "nominal interest rate" on the vertical axis, and plot the demand equation Qd = D(P,i) = 1000-5P -10i only.
(g) For each of the variables P,i, explain whether they cause movement along the Qd curve, or a shift in the Qd curve.