Consider the market for new, single-family homes in a mid-western town in the U.S.
The general demand function for new housing in the town is estimated to be
Qd = 15 - 2P + 0.05M + 0.10R
Where Qd is the monthly quantity demanded, P is the price per square foot, M is average monthly income in the town, and R is the average monthly rent for a three-bedroom apartment in the town. Qd is measured in units of 1,000 square feet per month. (6 pts each)
a. Is housing in this town a(n) normal or inferior good? Explain?
b. Are new housing and three-bedroom apartments substitutes or complements in this town? Explain?
c. Derive the demand function for new housing in the town when average monthly income is $1,500 and the monthly rental rate for three-bedroom apartments is $700.
The general supply function for new housing in the town is estimated to be
Qs = 96 + 2P - 10PL - 4Pk
Where P is the price per square foot of new housing in the town, PL is the average hourly wage rate for construction workers, and PK is the price of capital (as measured by the average rate of interest paid on loans to home builders). Qs is measured in units of 1,000 square feet per month.
d. Derive the supply function for new housing when the average hourly wage rate for construction workers is $10 per hour and the average rate of interest on loans to builders is 9%.
e. Solve mathematically for equilibrium price and quantity of new houses in the town