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Consumer Surplus. Demand function:. Demand Curve:. Demand Function and Demand Curve. Consider a demand function The inverse demand function is. Cobb-Douglas example:. Inverse Demand Function. Inverse Demand Curve. Optimal choice: Suppose: (composite good) Rearrange:.

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inverse demand function
Consider a demand function

The inverse demand function is

Cobb-Douglas example:

Inverse Demand Function
inverse demand curve
Inverse Demand Curve

Optimal choice:

Suppose:

(composite good)

Rearrange:

Inverse Demand Curve
gross consumer surplus
Gross Consumer Surplus
  • Consumer buys

units of good 1.

  • Consumer has different willingness to pay for each extra unit.
  • GCS: Area under demand curve.
  • GCS tells us how much money consumer willing to pay for
consumer surplus6
Consumer Surplus
  • Consumer buys

units of good 1.

  • Consumer pays

for each unit.

the welfare effect of changes in prices
The Welfare Effect of Changes in Prices
  • Goal: provide a monetary measure of the effects of price changes on the utility of the consumer.
  • 3 ways of doing it:
  • Compute changes in consumer’s surplus;
  • Compensating variation;
  • Equivalent variation.
change in consumer s surplus9
Change in Consumer’s Surplus
  • In practice, to compute the change in CS we need to have an estimate of the consumer’s demand function. This can be done using statistical methods.
  • How is change in CS related to change in utility? The two coincide when utility is quasi-linear:
compensating variation
CV=how much money we need to give the consumer after the price change to make him just as well off as he was before the price change.

Budget line:

Compensating Variation
equivalent variation
EV=how much money we need to take away from the consumer before the price change to make him just as well off as he was after the price change.

Budget line:

Equivalent Variation
compensating and equivalent variations
Compensating and Equivalent Variations
  • To compute CV and EV we need to know utility function of the consumer.
  • This can be estimated from the data by observing consumer’s demand behavior.
  • E.g. observe consumer’s choices at different prices and income levels. Observe that expenditures shares are relatively constant:

Cobb-Douglas preferences.

an example increase in oil prices
An Example: Increase in Oil Prices
  • Often, OPEC manages to restrict production and significantly increase oil prices.
  • What’s the effect of this increase on consumers’ welfare?
model
Model
  • Consumers’ utility function over gasoline and composite goods, :
  • Moreover:
find consumer demand s before price increase
Find Consumer Demand’s Before Price Increase
  • Consumer solves:
  • Optimality condition:
find consumer demand s before price increase16
Find Consumer Demand’s Before Price Increase
  • Since:
  • Demand for gasoline is:
  • Demand for composite good:
find consumer demand s after price increase
Find Consumer Demand’s After Price Increase
  • Since:
  • Demand for gasoline goes down:
  • Demand for composite good:
compute compensating variation
Compute Compensating Variation
  • Government pays amount CV such that:
  • Plug in numbers:
compute compensating variation20
Compute Compensating Variation
  • Plug in numbers:
  • Get:
compute equivalent variation
Compute Equivalent Variation
  • Government pays amount EV such that:
  • Plug in numbers:
compute equivalent variation22
Compute Equivalent Variation
  • Plug in numbers:
  • Get:
conclusion
Conclusion
  • In this case: change in consumer’s surplus equals compensating variation which equals equivalent variation.
  • In general these three measures differ.
this wednesday

This Wednesday:

Who Wants to be an Economist?