   Chapter 13.4, Problem 3CP ### 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

# If demand is p = 100 x + 1 , supply is p   =   x   + 1 , and the market equilibrium is (9, 10), create the integral used to find the(a) consumer's surplus. (b) producer's surplus.

To determine

To calculate: The integral of consumer’s surplus whose demand function is p=100(x+1) and supply function is p=x+1.

Explanation

Given Information:

The consumer’s surplus whose demand function is approximated by p=100(x+1) and supply function is p=x+1 and the market equilibrium is (9,10).

Formula used:

The consumer’s surplus for a demand function g(x) at equilibrium is,

CS=0x1g(x)dxp1x1

Where p1 is the equilibrium price ad x1 is the unit sold at equilibrium.

Calculation:

Consider the demand function, p=100(x+1) and supply function, p=x+1.

The equilibrium point (x1,p1) is given as:

x1=9p1=10

Use the formula for the consumer’s surplus for a demand function g(x) at equilibrium is,

CS=0x1g(x)dxp1x1

(b)

To determine

To calculate: The integral of producer’s surplus whose demand function is p=100(x+1) and supply function is p=x+1.

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