   Chapter 13, Problem 9T ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Suppose the supply function for a product is   p   = 40   +   0.001 x 2 and the demand function is p =   120   −   0.2 x , where x is the number of units and p is the price in dollars. If the market equilibrium price is $80, find (a) the consumer’s surplus and (b) the producer's surplus. (a) To determine To calculate: The consumer’s surplus for the supply function p=40+0.001x2 and demand function p=1200.2x, where x is the number of units and p is the price in dollars. The market’s equilibrium price is$80.

Explanation

Given information:

The provided supply function is p=40+0.001x2 and demand function is p=1200.2x, where x is the number of units and p is the price in dollars. The market’s equilibrium price is $80. Formula used: The consumer’s surplus is provided by CS=0x1f(x)dxp1x1, where p1 is the equilibrium price, x1 is the equilibrium quantity, the product p1x1 is total dollars spent by consumer and received as revenue by producers. Calculation: Consider the supply function, p=40+0.001x2 and the demand function, p=1200.2x. The market equilibrium price p is$80.

Substitute p=80 in the demand function p=1200.2x,

80=1200.2x80120=0.2x400

(b)

To determine

To calculate: The producer’s surplus for the supply function p=40+0.001x2 and demand function p=1200.2x, where x is the number of units and p is the price in dollars. The market’s equilibrium price is \$80.

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