   Chapter 13.4, Problem 27E ### 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 that the supply function for a good is p   =   4 x 2 + 2 x +   2 . If the equilibrium price is \$422 per unit, what is the producer’s surplus there?

To determine

To calculate: The producer’s surplus for a good whose supply function is approximated by p=4x2+2x+2 dollar and the equilibrium price is 422 dollars per unit.

Explanation

Given Information:

The producer’s surplus for a good whose supply function is approximated by p=4x2+2x+2 dollars. Where, the equilibrium price is 422 dollars per unit.

Formula used:

The producer’s surplus for a supply function g(x) at equilibrium is,

PS=p1x10x1g(x)dx.

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

Calculation:

Consider the supply function, p=4x2+2x+2.

The price of the unit at equilibrium is,

p=422

The provided supply function is given as,

p=4x2+2x+2

Substituting 422 for p in the supply function to get x1,

422=4x2+2x+24x2+2x420=02(2x+21)(x10)=0

Solve the further,

x=10

And

x=212 (Not Possible, since x cannot be negative)

Thus, the equilibrium point (x1,p1) is given as:

x1=10p1=422

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