   Chapter 13, Problem 45RE ### 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

# Producer's surplus Find the producers surplus at market equilibrium for Problem 44.Consumer's surplus The demand function for a product under pure competition is p = 64 − 4 x , and the supply function is p   =   x   − 1 , where x is the number of units and p is in dollars.(a) Find the market equilibrium.(b) Find the consumer’s surplus at market equilibrium.

To determine

To calculate: The producer’s surplus at market equilibrium if the demand function of a product is provided by p=644x and the supply function is p=x1, where x is the number of units and p is the in dollars.

Explanation

Given Information:

The demand function of a product is provided by p=644x and the supply function is p=x1, where x is the number of units and p is the in dollars.

Formula used:

If the demand curve is p=f(x) and the supply curve is p=g(x) then at the point of equilibrium,

f(x)=g(x)

The producer’s surplus is provided by PS=p1x10x1g(x)dx, where p1 is the equilibrium price, x1 is the equilibrium quantity, the product p1x1 is total revenue at the equilibrium point.

According to the power rule of integrals,

xndx=xn+1n+1+C, where n1.

Calculation:

Consider the demand function, p=644x and the supply function, p=x1.

Now, at equilibrium point, the demand function and supply function must be equal.

644x=x1

Take square on both sides,

(644x)2=(x1)2644x=x22x+10=x2+2x630=(x+9)(x7)

This gives the values x=9, x=7

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