Consumer Surplus: Understanding the Economic Concept and Its Measurement, Study notes of Customer Relationship Management (CRM)

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Consumer Surplus

Demand Function and DemandCurve Demand function:

Demand Curve:

) m p p x x

,

,

2

1

1

1

=

1

p

1 x

Inverse Demand Curve

Inverse Demand Curve

1

p

1 x

Optimal choice: Suppose:(composite good) Rearrange:

1

2

=

p

MRS

p p

−

=

1 2

MRS

p

−

=

1

0

• 1 x * 1 p

Gross Consumer Surplus Consumer buysunits of good 1. Consumer has differentwillingness to pay for eachextra unit. GCS: Area under demandcurve. GCS tells us how muchmoney consumer willingto pay for

1

p

1

x

0

• 1 x 1 * x 1 * x

The Welfare Effect of Changes inPrices

Goal: provide a monetary measure of theeffects of price changes on the utility ofthe consumer. 3 ways of doing it:

Compute changes in consumer’s surplus;

Compensating variation;

Equivalent variation.

Change in Consumer’s Surplus Suppose a taxincreases price ofgood 1 from

to

.

Decrease in CS:

1 p

1 p

1 p

1 p

1 x

1 x

1 x

1

p

R

T

T

R

Compensating Variation CV=how much moneywe need to give theconsumer

after

the

price change to makehim just as well off ashe was

before

the

price change. Budget line:

1 x

2 x

X

Y

Z

1

1

2

x

p

m

x

−

=

CV

Equivalent Variation EV=how much moneywe need to take awayfrom the consumer before

the price

change to make himjust as well off as hewas

after

the price

change. Budget line:

1 x

2 x

X

Y

Z

1

1

2

x

p

m

x

−

=

EV

An Example: Increase in OilPrices Often, OPEC managesto restrict productionand significantlyincrease oil prices. What’s the effect ofthis increase onconsumers’ welfare?

Model Consumers’ utility function over gasolineand composite goods,

:

Moreover:

(

)

(

)

2

1 2

1

2

1

x

x

x

x

u

1

x

2

x

1

1

p

p m

Find Consumer Demand’s BeforePrice Increase Since: Demand for gasoline is: Demand for composite good:

(

)

2

1

1

p

x

1

p

2

x

Find Consumer Demand’s AfterPrice Increase Since: Demand for gasoline goes down: Demand for composite good:

(

)

2

1

1

p

x

1

p

2

x

Compute CompensatingVariation Government pays amount CV such that: Plug in numbers:

  

  

=

CV

u

u

5 .

187 ,

4 25

175 ,

25

(

)

CV

1 2

1 2

Compute CompensatingVariation Plug in numbers: Get:

(

)

EV

1 2

1 2

EV