   Chapter 13.4, Problem 30E ### 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 the supply function for a commodity is p =   40   +   100 ( x +   1   ) 2 , what is the producer's surplus at x = 20?

To determine

To calculate: The producer’s surplus for a good whose supply function is approximated by p=40+100(x+1)2 dollars and the equilibrium quantity is 20 unit to be sale.

Explanation

Given Information:

The producer’s surplus for a good whose supply function is approximated by p=40+100(x+1)2 dollars and the equilibrium quantity is 20 unit to be sale.

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=40+100(x+1)2 and the number of units x sold is 20.

The provided supply function is given as,

p=40+100(x+1)2

Substituting the value x=20 in the supply function to get p1:

p=40+100(20+1)2=40+100(21)2=40+44,100=44,140

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

x1=20p1=44,140

Use the formula for the producer’s surplus,

PS=p1x10x1g(x)dx

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