Question

The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation 

p = 164-x² 

where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is 

p = 68+1/2x² 

dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. (Round your answers to the nearest dollar.) 

consumer's surplus $_______ 

 producer's surplus $_______ 

Answer 1

In equilibrium, demand price equals supply price.

164 - x² = 68 + (x²/2)

3x²/2 = 96

x² = 96 x (2/3) = 64

x = 8

p = 164 - (8 x 8) = 164 - 64 = 100

From demand function, when x = 0, p = 164 (Vertical intercept of demand curve).

Consumer surplus = Area between demand curve and price = (1/2) x (164 - 100) x 8 = 4 x 64 = 256

From supply function, when x = 0, p = 68 (Vertical intercept of supply curve).

Producer surplus = Area between supply curve and price = (1/2) x (100 - 68) x 8 = 4 x 32 = 128