Finance 510 microeconomic analysis
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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

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Finance 510 microeconomic analysis

Finance 510: Microeconomic Analysis

Consumer Demand Analysis


Finance 510 microeconomic 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?


Finance 510 microeconomic analysis

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!


Finance 510 microeconomic analysis

What about this choice?

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


Finance 510 microeconomic analysis

Is strictly preferred to

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


Finance 510 microeconomic analysis

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”


Finance 510 microeconomic analysis

Using the previous example (Recall, C > B > 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


Finance 510 microeconomic analysis

  • We only require a couple restrictions on Utility functions

    • 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)


Finance 510 microeconomic analysis

Suppose we have the following utility function

U = 20

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


Finance 510 microeconomic analysis

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


Finance 510 microeconomic analysis

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


Finance 510 microeconomic analysis

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


Finance 510 microeconomic analysis

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?


Finance 510 microeconomic analysis

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


Finance 510 microeconomic analysis

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


Finance 510 microeconomic analysis

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)!


Finance 510 microeconomic analysis

An Example


Finance 510 microeconomic analysis

The elasticity of substitution measures the curvature of the indifference curve


Finance 510 microeconomic analysis

An Example


Finance 510 microeconomic analysis

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

As before, set up the lagrangian…


Finance 510 microeconomic analysis

First Order Necessary Conditions


Finance 510 microeconomic analysis

Suppose that we raise the price of X

Can we be sure that demand for x will fall?


Finance 510 microeconomic analysis

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


Finance 510 microeconomic analysis

Now, take that extra income away…

Income effect


Finance 510 microeconomic analysis

Demand Curves present the same information in a different format

D


Finance 510 microeconomic analysis

Demand Curves present the same information in a different format


Finance 510 microeconomic analysis

Elasticity of Substitution vs. Price Elasticity


Finance 510 microeconomic analysis

Perfect Complements vs. Perfect Substitutes

(Almost)


Finance 510 microeconomic analysis

Suppose that we raise the price of Y…

Substitution effect (+)

Income effect (-)

Net Effect = ????


Finance 510 microeconomic analysis

Cross Price Elasticity


Finance 510 microeconomic analysis

Income and Substitution effects cancel each other out!!


Finance 510 microeconomic analysis

Suppose that we raise Income

Substitution effect = 0

Income effect (-)


Finance 510 microeconomic analysis

Income Elasticity


Finance 510 microeconomic analysis

Willingness to pay

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


Finance 510 microeconomic analysis

Willingness to pay

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


Finance 510 microeconomic analysis

Consumer Surplus

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


Finance 510 microeconomic analysis

Consumer Surplus

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


Finance 510 microeconomic analysis

A useful tool…

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


Finance 510 microeconomic analysis

Estimating demand curves

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


Finance 510 microeconomic analysis

High Elasticity

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

Low Elasticity


Finance 510 microeconomic analysis

Estimating demand curves

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


Finance 510 microeconomic analysis

Estimating demand curves

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


Finance 510 microeconomic analysis

Estimating demand curves

The most common is a log-linear demand curve:

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


Finance 510 microeconomic analysis

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


Finance 510 microeconomic analysis

Estimating demand curves

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

D


Finance 510 microeconomic analysis

Estimating demand curves

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


Finance 510 microeconomic analysis

Estimating demand curves

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


Finance 510 microeconomic analysis

An example…

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


Finance 510 microeconomic analysis

Suppose we solved for price and quantity by using the equilibrium condition


Finance 510 microeconomic analysis

We could estimate the following equations

The original parameters are related as follows:

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


Finance 510 microeconomic analysis

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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