Question: Below is a mathematical demand function for new Cadillac’s sold per year for a dealer.

\[{{Q}_{C}}=200-0.01{{P}_{C}}+0.005{{P}_{L}}-10{{P}_{G}}+0.01Y+0.003A\] where:

P_C = the average price of Cadillac’s

P_L = the average price of Lincoln Continentals

P_G = the price of gasoline

Y = the average family income

A = dollars spent annually on advertising.

(a) Find the point price elasticity of demand if P_C = $11,000, P_L = $10,000, P_G = $0.60

Y= $6,000, and A = $2,000.

(b) Is the price elasticity of demand elastic, unitary elastic, or inelastic? Why?

(c) Find the arc cross elasticity of demand for Cadillac’s and Continentals between P_L = $10,000 and P_L = $9,000. [All other figures except Q, remain the same as part (a)

(d) Are Cadillac’s and Lincolns substitutes or complements? Why?