Question

1. Assume that the functional form for new homes in a community each year is as follows:

Q_d = 1025 – (10*P) + (3*P_e) + (.25*P_r) + (8*Y) + (25*F) - (.75*T)

            And take the following values as constant:

                        P_e = 100 (in thousands of $)

                        P_r = 700 (in dollars per month)

                        Y = 45 (in thousands of $ per year)

                        F = 2.8 (in persons per household)

                        T = 120 (in $ of tax per home per year)

(The demand equation requires variables in the units mentioned for each of the five variables)

Solve for the reduced form linear demand function.

2. Turning to supply, assume that the price of new housing (P), the price of building materials (P_m), the wages of construction workers (W), the price of undeveloped land (P_u), and the level of impact fees they must pay to build a new house (IF) all affect the amount firms are willing to supply new homes. Take the specific functional form to be:

Q_s = 100 + (12*P) – (8*P_m) – (20*W) – (8*P_u) – (10*IF)

And take the following values as constant and given:

P_m = 30 (in thousands of $ per house)

W = 18 (in $ per hour)

P_u = 15 (in thousands of $ per lot)

IF = 4 (in thousands of $ per new house)

(The supply equation requires variables in the units mentioned for each of the four variables)

Solve for the reduced form linear supply function.

3. Using the reduced form Linear Demand & Supply functions you found in problems 1 & 2, solve for the equilibrium price (P) and quantity (Q) in this market. If either does not turn out to be an integer, please round to one decimal point.

4. Mathematically derive an equation that shows how the price of new homes (P) varies with the price of existing homes (P_e). Assume all variables other than P_e are held constant at the values given in problems 1 & 2.

Answer 1