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Finance 510: Microeconomic Analysis. Consumer Demand Analysis. Suppose that you observed the following consumer behavior. P(Bananas) = $4/lb. P(Apples) = $2/Lb. Q(Bananas) = 10lbs Q(Apples) = 20lbs. Choice A. P(Bananas) = $3/lb. P(Apples) = $3/Lb. Q(Bananas) = 15lbs Q(Apples) = 15lbs.

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Finance 510 microeconomic analysis

Finance 510: Microeconomic Analysis

Consumer Demand Analysis


Suppose that you observed the following consumer behavior

P(Bananas) = $4/lb.

P(Apples) = $2/Lb.

Q(Bananas) = 10lbs

Q(Apples) = 20lbs

Choice A

P(Bananas) = $3/lb.

P(Apples) = $3/Lb.

Q(Bananas) = 15lbs

Q(Apples) = 15lbs

Choice B

What can you say about this consumer?

Is strictly preferred to

Choice B

Choice A

How do we know this?


Consumers reveal their preferences through their observed choices!

Q(Bananas) = 10lbs

Q(Apples) = 20lbs

Q(Bananas) = 15lbs

Q(Apples) = 15lbs

P(Bananas) = $4/lb.

P(Apples) = $2/Lb.

Cost = $80

Cost = $90

P(Bananas) = $3/lb.

P(Apples) = $3/Lb.

Cost = $90

Cost = $90

B Was chosen even though A was the same price!


What about this choice? choices!

Choice C

Cost = $90

P(Bananas) = $2/lb.

P(Apples) = $4/Lb.

Q(Bananas) = 25lbs

Q(Apples) = 10lbs

Q(Bananas) = 15lbs

Q(Apples) = 15lbs

Cost = $90

Choice B

Q(Bananas) = 10lbs

Q(Apples) = 20lbs

Cost = $100

Choice A

Is strictly preferred to

Is choice C preferred to choice A?

Choice C

Choice B


Is strictly preferred to choices!

Choice B

Choice A

Is strictly preferred to

Choice C

Choice B

C > B > A

Is strictly preferred to

Choice C

Choice A

Rational preferences exhibit transitivity


Consumer theory begins with the assumption that every consumer has preferences over various consumer goods. Its usually convenient to represent these preferences with a utility function

Set of possible choices

“Utility Value”


Using the previous example (Recall, C > B > A) consumer has preferences over various consumer goods. Its usually convenient to represent these preferences with a

Choice A

Q(Bananas) = 10lbs

Q(Apples) = 20lbs

Choice B

Q(Bananas) = 15lbs

Q(Apples) = 15lbs

Choice C

Q(Bananas) = 25lbs

Q(Apples) = 10lbs


  • We only require a couple restrictions on Utility functions consumer has preferences over various consumer goods. Its usually convenient to represent these preferences with a

    • For any two choices (X and Y), either U(X) > (Y), U(Y) > U(X), or U(X) = U(Y) (i.e. any two choices can be compared)

    • For choices X, Y, and Z, if U(X) > U(Y), and U(Y) > U(Z), then U(X) > U(Z) (i.e., the is a definitive ranking of choices)

  • However, we usually add a couple additional restrictions to insure “nice” results

    • If X > Y, then U(X) > U(Y) (More is always better)

    • If U(X) = U(Y) then any combination of X and Y is preferred to either X or Y (People prefer moderation to extremes)


Suppose we have the following utility function consumer has preferences over various consumer goods. Its usually convenient to represent these preferences with a

U = 20

Imagine taking a “cross section” at some utility level.


The “cross section” is called an indifference curve (various combinations of X and Y that provide the same level of utility)

Any two choices can be compared

There is a definite ranking of all choices

A

C

B


The “cross section” is called an indifference curve (various combinations of X and Y that provide the same level of utility)

More is always better!

C

A

B


The “cross section” is called an indifference curve (various combinations of X and Y that provide the same level of utility)

People Prefer Moderation!

A

C

B


The marginal rate of substitution (MRS) measures the amount of Y you are willing to give up in order to acquire a little more of X

+

= 0

Suppose you are given a little extra of good X. How much Y is needed to return to the original indifference curve?


The marginal rate of substitution (MRS) measures the amount of Y you are willing to give up in order to acquire a little more of X

+

= 0

Now, let the change in X become arbitrarily small


The marginal rate of substitution (MRS) measures the amount of Y you are willing to give up in order to acquire a little more of X

Marginal Utility of X

Marginal Utility of Y


The marginal rate of substitution (MRS) measures the amount of Y you are willing to give up in order to acquire a little more of X

If you have a lot of X relative to Y, then X is much less valuable than Y MRS is low)!


An Example of Y you are willing to give up in order to acquire a little more of X



An Example indifference curve


Consumers solve a constrained maximization – maximize utility subject to an income constraint.

As before, set up the lagrangian…


First Order Necessary Conditions utility subject to an income constraint.


Suppose that we raise the price of X utility subject to an income constraint.

Can we be sure that demand for x will fall?


Suppose that we raise the price of X, but at the same time, increase your income just enough so that your utility is unchanged

Substitution effect


Now, take that extra income away… increase your income just enough so that your utility is unchanged

Income effect






Suppose that we raise the price of Y… format

Substitution effect (+)

Income effect (-)

Net Effect = ????




Suppose that we raise Income format

Substitution effect = 0

Income effect (-)



Willingness to pay format

Suppose that we have the following demand curve

$100

A demand curve tells you the maximum a consumer was willing to pay for every quantity purchased.

$50

D

100

For the 100th sale of this product, the maximum anyone was willing to pay was $50


Willingness to pay format

Suppose that we have the following demand curve

$100

$75

$50

D

50

100

For the 50th sale of this product, the maximum anyone was willing to pay was $75


Consumer Surplus format

Consumer surplus measures the difference between willingness to pay and actual price paid

$100

$75

Whoever purchased the 50th unit of this product earned a consumer surplus of $25

$50

D

50

100

For the 50th sale of this product, the maximum anyone was willing to pay was $75


Consumer Surplus format

Consumer surplus measures the difference between willingness to pay and actual price paid

$100

If we add up that surplus over all consumers, we get:

CS = (1/2)($100-$50)(100-0)=$2500

$2500

$50

Total Willingness to Pay ($7500)

$5000

- Actual Amount Paid ($5000)

D

Consumer Surplus ($2500)

100


A useful tool… format

In economics, we are often interested in elasticity as a measure of responsiveness (price, income, etc.)


Estimating demand curves format

Given our model of demand as a function of income, and prices, we could specify a demand curve as follows:


High Elasticity format

Linear demand has a constant slope, but a changing elasticity!!

Low Elasticity


Estimating demand curves format

We could, instead, use a semi-log equation:


Estimating demand curves format

We could, instead, use a semi-log equation:


Estimating demand curves format

The most common is a log-linear demand curve:

Log linear demand curves are not straight lines, but have constant elasticities!


If we assumed that this was the maximization problem underlying a demand curve, what form would we use to estimate it?


Estimating demand curves underlying a demand curve, what form would we use to estimate it?

Suppose you observed the following data points. Could you estimate the demand curve?

D


Estimating demand curves underlying a demand curve, what form would we use to estimate it?

A bigger problem with estimating demand curves is the simultaneity problem.

S

Market prices are the result of the interaction between demand and supply!!

D


Estimating demand curves underlying a demand curve, what form would we use to estimate it?

Case #1: Both supply and demand shifts!!

Case #2: All the points are due to supply shifts

S

S

S’

S’

S’’

S’’

D

D’

D’’

D


An example… underlying a demand curve, what form would we use to estimate it?

Suppose you get a random shock to demand

Demand

The shock effects quantity demanded which (due to the equilibrium condition influences price!

Supply

Therefore, price and the error term are correlated! A big problem !!

Equilibrium



We could estimate the following equations equilibrium condition

The original parameters are related as follows:

We can solve for the supply parameter, but not demand. Why?


By including a demand shifter (Income), we are able to identify demand shifts and, hence, trace out the supply curve!!

S

D

D

D


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