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
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?
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
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)
Choice A
Q(Bananas) = 10lbs
Q(Apples) = 20lbs
Choice B
Q(Bananas) = 15lbs
Q(Apples) = 15lbs
Choice C
Q(Bananas) = 25lbs
Q(Apples) = 10lbs
Suppose we have the following utility function
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
The elasticity of substitution measures the curvature of the indifference curve
An Example
Consumers solve a constrained maximization – maximize utility subject to an income constraint.
As before, set up the lagrangian…
First Order Necessary Conditions
Suppose that we raise the price of X
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…
Income effect
Demand Curves present the same information in a different format
D
Demand Curves present the same information in a different format
Elasticity of Substitution vs. Price Elasticity
Perfect Complements vs. Perfect Substitutes
(Almost)
Suppose that we raise the price of Y…
Substitution effect (+)
Income effect (-)
Net Effect = ????
Cross Price Elasticity
Income and Substitution effects cancel each other out!!
Suppose that we raise Income
Substitution effect = 0
Income effect (-)
Income Elasticity
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
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
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
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
A useful tool…
In economics, we are often interested in elasticity as a measure of responsiveness (price, income, etc.)
Estimating demand curves
Given our model of demand as a function of income, and prices, we could specify a demand curve as follows:
High Elasticity
Linear demand has a constant slope, but a changing elasticity!!
Low Elasticity
Estimating demand curves
We could, instead, use a semi-log equation:
Estimating demand curves
We could, instead, use a semi-log equation:
Estimating demand curves
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
Suppose you observed the following data points. Could you estimate the demand curve?
D
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
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
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
Suppose we solved for price and quantity by using the equilibrium condition
We could estimate the following equations
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