   Chapter 5, Problem 20TYS ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# The demand and supply functions for a product are modeled byDemand: p =   − 0.625 x   +   10 and Supply: p =   0.25 x   +   3 where p is the price (in dollars) and x is the number of units (in millions). Find the consumer and producer surpluses for this product.

To determine

To calculate: The consumer and producer surpluses if the demand function is p=0.625x+10 and supply function is p=0.25x+3.

Explanation

Given information:

The demand function is p=0.625x+10 and supply function is p=0.25x+3.

Formula used:

Basic integration rule,

xndx=xn+1n+1+c

Consumer surplus is defined as,

0x(demand function price)dx

Where x is the number of units.

Producer surplus,

0x(pricesupply function)dx

Where x is the number of units.

Calculation:

Consider the demand function p=0.625x+10 and supply function p=0.25x+3

Equate the demand and supply functions to determine the equilibrium point.

0.625x+10=0.25x+30.875x=7x=8

Substitute the x for 8 in p=0.25x+3

p=0.25x+3=0.25(8)+3=5

The price is \$5

To find the consumer surplus by the use the formula,

0x(demand function price)dx=08[(0.625x+10)5]dx=08(0.625x+5)dx=[0

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