   Chapter 13, Problem 49RE ### 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 Suppose the supply function for x units of a certain lamp is given by p = 0.02 x + 50.01 − 10 x 2 + 1 where p is in dollars. Find the producer's surplus if the equilibrium price is $70 and the equilibrium quantity is 1000. To determine To calculate: The Producer’s Surplus for a good where supply function for x units of a certain lamp is p=0.02x+50.0110x21 dollars, p in dollars and the equilibrium price is$70 and the equilibrium quantity is 1000.

Explanation

Given Information:

The supply function for x units of a certain lamp is p=0.02x+50.0110x21 dollars, p in dollars and the equilibrium price is \$70 and the equilibrium quantity is 1000.

Formula used:

According to the Producer’s Surplus,

The producer surplus is given by the area between p=g(x) and the x axis from 0 to x1, subtracted from p1x1 if the supply function is p=g(x),

PS=p1x10x1g(x)dx

Calculation:

Consider the supply function,

p=0.02x+50.0110x21

Here p1=70 and x1=1000, also g(x)=0.02x+50.0110x21

Use the formula of producer surplus to calculate the producer surplus as,

PS=(70)(1000)01000(0

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