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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

In Problems 17-26, p and C are in dollars and x is the number of units.

If the demand function for a product is p   =  1 2 / ( x +   1 ) and the supply function is p =   1   +   0.2 x , find the consumer’s surplus under pure competition.

To determine

To calculate: The Consumer’s Surplus under pure competition for a product whose demand function is approximated by p=12(x+1) and supply function is p=1+0.2x.

Explanation

Given Information:

Demand function is approximated by p=12(x+1) and

Supply function is p=1+0.2x.

Formula used:

According to the Consumer’s Surplus:

If the demand curve has equation p=f(x), the consumer surplus is given by the area between f(x) and the x-axis from 0 to x1, less the area of TR is,

CS=0x1f(x)dxp1x1.

Calculation:

Consider the demand function:

p=12(x+1)

Since, to know the equilibrium point:

 Demand Function =Supply Function

Now equate both the equations,

12(x+1)=1+0.2x12=1+1.2x+0.2x22x2+12x110=02(x+11)(x5)=0

Simplify further for the value of x,

x=5

And

x=11 (Not possible, since x can’t be negative)

Substitute x=5 in the demand function to get p1,

p=12(5+1)=126

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Chapter 13 Solutions

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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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