Question

In May 1991, Car and Driver described a Jaguar that sold for 980,000 dollars. Suppose that at that price only 45 have been sold. If it is estimated that 350 could have been sold if the price had been 500,000 dollars. Assuming that the demand curve is a straight line, and that 500,000 dollars and 350 are the equilibrium price and quantity, find the consumer surplus at the equilibrium price.
surplus = ?? thousands of dollars(Using Calculus)

Answer 1

Equation of the demand curve is

(P - 500000)/(Q-350) = (980000-500000)/(45-350)

When Q=0, price is P = 500000 - 350*(980000-500000)/(45-350) = 1,050,819.67

So, consumer surplus at equilibrium

= 0.5*350*(1,050,819.67 - 500,000)
= 96,393,443

which is about 96393 thousands of dollars