   Chapter 13, Problem 44RE ### 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

# 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.

(a)

To determine

To calculate: The 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)

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<

(b)

To determine

To calculate: The consumer’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.

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