Question

Prices of Homes in California Plunge in the Late 2000s

A major consequence of the housing market crisis has been a significant decline in the home prices

as foreclosures intensified between 2007 and 2008. One of the hardest states hit was California. The median price of a new home in California decreased by 35.3 percent from August 2007 to August 2008. Interestingly, the quantity of homes sold was 13.6 percent higher in August 2008 than in August 2007.

What was the price elasticity of demand for homes in California in the period under examination? Price elasticity of demand is defined as the absolute value of the percentage change in quantity demanded divided by the percentage change in price; in this case, 13.6% ¸ 35.3% = 0.39.

QUESTION: Did Californians spend more or less on homes in August 2007 or in August 2008?

Answer 1

Given,

Let the median price of a new home in California in 2007 be P

Let the quantity of new homes purchases in California be Q

Total spending on new homes by Californians in 2007 = P*Q = PQ

The median price of a new home decreased by 35.3% from 2007 to 2008

Median price of a new home in 2008 = (1 - 35.3/100) * P = 0.647P

Quantity of homes purchased increased by 13.6% from 2007 to 2008

Quantity of homes purchased in 2008 = (1 + 13.6/100) * Q = 1.136Q

Total spending on new homes purchases by Californians in 2008 = 0.647P * 1.136Q = 0.73 PQ = 0.73 times the total spending on homes by Californians in 2007

(It can also be determined through the elasticity of demand. If the demand is elastic, a decrease in the price increases the total revenue and if the demand is inelastic, a decrease in price decreases the total revenue)

Therefore, the Californians spent more on new homes in August 2007 and less on new homes in August 2008.