   Chapter 13.4, Problem 29E ### 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   =   10 e x / 3 , what is the producers surplus when 15 units are sold?

To determine

To calculate: The producer’s surplus for a good whose supply function is approximated by p=10ex3 dollars. Where, the equilibrium quantity is 15 unit to be sale.

Explanation

Given Information:

The producer’s surplus for a good whose supply function is approximated by p=10ex3 dollars. Where, the equilibrium quantity is 15 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=10ex3 and the number of unit x is 15.

The provided supply function is,

p=10ex3

Substituting 15 for x in the supply function to get p1:

p=10e153=10e5=1484.13

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

x1=15p1=1484.13

Use the formula for the producer’s surplus,

PS=p1x10x1g(x)dx

Substituting 15 for x1, 1484

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