Chapter 6.7, Problem 1TE

Re-solve Example 1, Section 6.7, using a graphing utility.

Hint: Use the intersection operation to find the equilibrium quantity and the equilibrium price. Use the numerical integral operation to evaluate the definite integral.

EXAMPLE 1

The demand function for a certain make of ten-speed bicycle is given by

p = D(x) = −0.001 x² + 250

where p is the unit price in dollars and x is the quantity demanded in thousands of units. The supply function for these bicycles is given by

p = S(x) = 0.0006x² + 0.02x + 100

where p stands for the unit price in dollars and x stands for the number of bicycles that the supplier will put on the market, in units of a thousand. Determine the consumers’ surplus and the producers’ surplus if the market price of a bicycle is set at the equilibrium price.