Section 6.7 topic: Consumers’ and Producers’ Surplus

Consumers’ Surplus: If p = D(x) is the demand equation, p

o

is the equilibrium price of the com-

modity, and x

o

is the equilibrium quantity, then the consumers’ surplus is given by

Zx

o

0

[D(x)� p

o

] dx

Producers’ Surplus: If p = S(x) is the supply equation, p

o

is the equilibrium price of the commodity,

and x

o

is the equilibrium quantity, then the producers’ surplus is given by

Zx

o

0

[p

o

� S(x)] dx

1. Determine the producers’ surplus for the supply function below at the given number of units sold.

(Round answer to two decimal places.)

p = S(x) = 80e

0.06x, x

o

= 30

2. Calculate the consumers’ surplus for the demand equation at the given number of units demanded.

(Round answer to the nearest cent.)

p = D(x) = 272x

1/3, x

o

= 343

3. Determine the consumers’ surplus and the producers’ surplus at the equilibrium price level for

the following demand and supply functions. (Round answers to the nearest cent.)

p = D(x) = 83.1� 1.8x

p = S(x) = 0.3x

2+ 9

2 Fall 2016, Maya Johnson

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4. Calculate the producers’ surplus at the indicated price level for the supply equation below. (Round

answer to the nearest cent.)

p = S(x) = 130 + 0.2x

2, p

o

= 194.80

5. A fast-food outlet finds that the demand equation for its new side dish is given by

p = D(X) =

54

(x+ 1)

2

where p is the price (in cents) per serving and x is the number of servings that can be sold per

hour at this price. At the same time, the franchise is prepared to supply x servings per hour at

a price of p cents based on the supply function given by

p = S(x) = 2x+ 2

Find the equilibrium price, the consumers’ surplus CS and the producers’ surplus PS at this price

level.

3 Fall 2016, Maya Johnson