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Intermediate Microeconomic Theory

Demand

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Demand Analysis

In analyzing individual’s behavior regarding a given good, we start with a consumer’s demand function for that good.

q1(p1,p2,m)

Recall that a demand function was derived from “first principles”, or the explicit model of preferences and choice given a budget constraint (remember our underlying assumptions?).

However, in the end, it is this derived demand function that tells us all we need to know about consumer behavior.

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Engel Curves

We often want to describe how demand for a good changes as income changes. To do so, we use:

Engel Curve – shows how quantity demanded for a given good changes as income changes, holding prices constant.

How do we derive this graphically for good 1 given some set preferences and prices (e.g. p1=5 and p2=10)?

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Deriving Engel Curve Analytically

Straightforward given a utility function and prices. Example: Suppose again p1 = 5, p2 = 10 and utility

function given by U(q1,q2) = q10.5q2

0.5 .

What will be the equation for his Engel Curve for good 1?

Do these make sense?

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Engel Curves

What would happen to the Engel Curve for a given good if prices changed? Taking previous example, what if price of good 1 rose to $10/unit?

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Engel Curves

How about Engel curve given linear preferences (U(q1,q2) = q1 + q2)?

How about Engel curve given quasi-linear preferences (U(q1,q2) = q1

0.5 + q2) ?

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Further Characterizing Relationship between Demand and Income Normal Good – quantity demanded of

good rises with income, or

How would we show this graphically in a choice framework?

What does it imply about slope of Engel Curve?

Examples of normal goods?

0),,( 211

m

mppq

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Further Characterizing Relationship between Demand and Income Inferior Good - quantity demanded

decreases as income increases, or

Is this possible? How would we show this graphically in a choice framework?

What does it imply about slope of Engel Curve?

Examples of inferior goods?

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m

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The Slope of the Engel Curve

The slope of the Engel Curve is informative beyond just being positive or negative. Consider the Engel Curve shown below.

What does linearity imply (sometimes referred to as homothesticity)?

Do Cobb-Douglas preferences imply such a linear Engel curve?

m

q1

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The Slope of the Engel Curve

The slope of the Engel Curve don’t have to be constant. Consider the Engel Curve shown below.

What does concave shape imply?

What might be examples of goods with such an Engel curve? What is a good term to describe such goods?

m

q1

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The Slope of the Engel Curve

Consider the Engel Curve with convex shape.

What does convex shape imply (hint: consider Engel curve for quasi-linear preferences)?

What might be examples of goods with such an Engel curve? What is a good term to describe such goods?

m

q1

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Relevance of Engel Curve?

Why might understanding what Engel Curves are, and estimating their shape for different goods be important?

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Demand Curves

We also often want to describe how demand changes as price changes. To do so, we use:

Demand Curve – shows how quantity demanded for a given good changes as its price changes, holding other prices and income constant.

How do we derive this graphically for good 1 given some set preferences given p2=4 and m=24?

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Deriving a Demand Curve Analytically

Also straightforward given a utility function, prices of other goods, and income. Example: Suppose prices are m = 24, p2 = 4 and an

individual has a utility function U(q1,q2) = q10.5q2

0.5 .

What will be the equation for his Demand Curve for good 1?

Does this make sense? What will it look like?

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Demand Curves

Slope of demand curve indicates how much quantity demanded reacts to price. Generally, demand curves will be

downward sloping, meaning as price rises demand falls, or

We saw this will be the case with Cobb-Douglas specification of preferences. How about with linear utility function?

Given our assumptions, is it possible for a demand curve to slope upward?

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1

211

p

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Demand Curves

A good with an upward sloping demand curve is called a Giffen good (i.e. demand increases as price goes up and vice versa) Essentially, a Giffen good is an extremely inferior good.

“As Mr. Giffen has pointed out, a rise in the price of bread makes so large a drain on the resources of the poor labouring families and raises so much the marginal utility of money to them, that they are forced to curtail their consumption of meat and the more expensive foods: and, bread being still the cheapest food which they can get and will take, they consume more, and not less of it.”

-Alfred Marshall (1895)

While Giffen goods were known to be theoretically possible, no one had proven the existence of one, until…

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Demand Curves

Jensen and Miller (2008), “Giffen Behavior and Subsistence Consumption” American Economic Review

Argue that Giffen behavior is most likely to occur when: Households are poor enough that they face subsistence nutrition

concerns. Households consume a very simple diet, including a basic staple and a

“fancy” good. the basic good is cheapest source of calories available, comprises a

large part of diet/budget, and has no ready substitutes. Households cannot be so impoverished that they consume only the

staple good.

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Demand Curves

Conducted a field experiment Randomly chose households given vouchers that subsidized primary staple

(rice or wheat), which lowered the effective price of that good. Looked at consumption behavior between those given voucher and those

who weren’t. Find an inverted U-shape pattern of consumption of staples for poor

populations.

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Gross Substitutes and Complements

We have already discussed perfect substitutes and perfect complements.

We can now consider more nuanced definitions of substitutes and complements, with perfect versions being subsets.

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Gross Substitutes and Complements

Beer and pizza. Generally, I like to consume them together, one

beer with every slice. However, if the price of a slice went to $10, I

might behave a little differently. Some degree of complementarity, but not

perfect.

Pizza and Chicken Wings. A raise in the price of one would definitely cause

me to consume less of it and more of the other. However, they aren’t perfect substitutes. Even if

pizza was cheaper, I still might order a few chicken wings.

Some degree of substitutability between them but not perfect.

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Gross Substitutes and Complements

Gross substitutes - a rise in the price of one increases the quantity demanded for the other, or if

How would we show this graphically?

Consider skiing and golf. Suppose the price of lift tickets increased. How will the demand for golf course

time be affected? How about the demand curve for

golf course time?

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2

211

p

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Gross Substitutes and Complements

Gross complements - a rise in the price of one decreases the quantity demanded for the other, or if

How would we show this graphically?

Consider skiing and plane tickets. Suppose the price of lift tickets increased. How will the demand for a plane

ticket to SLC be affected? How about the demand curve?

0),,(

2

211

p

mppq

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Gross Substitutes and Complements

If someone’s preferences over two goods are captured by a Cobb-Douglas Utility function, will the two goods be gross substitutes, gross compliments, or neither?

How about if someone’s preferences are modeled using a quasi-linear utility function?

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Demand Curve and changes in income

Consider the Demand Curve for good 1 for an individual with Cobb-Douglas Utility U(q1,q2) = q1

0.6q20.4 , who has m = 20 and p2

= 4.

How would this Demand Curve be affected by a change in endowment from m = 20 to m = 30?

What if preferences were such that good 1 was an inferior good?

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Summary

Engel curves and Demand curves are derived from demand function (which is in turn derived from underlying preferences).

A Demand curve for a given good describes how the quantity demanded for that good changes as its own price changes, holding other prices and endowment fixed. Changes in prices of other goods or endowment may shift a

Demand curve.

An Engel curve for a given good describes how the quantity demanded for that good changes as income changes, holding other prices fixed. Changes in prices may shift an Engel curve.

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Summary

This means that: The change in quantity demanded for good i in

reaction to a change in the price of good i is captured by a movement along the demand curve for good i.

The change in quantity demanded for good i in reaction to change in price of some other good j or change in income is captured by a shift in the demand curve for good i.

Similarly, The change in quantity demanded for good i in

reaction to a change in income is captured by a movement along the Engel curve for good i.

The change in quantity demanded for good i in reaction to change in price of good i or another good j is captured by a shift in the Engel curve for good i.