Define income and substitution effects. - Income effect is the change in consumption
due to the change in purchasing power from a price change.
Substitution effect is a change in consumption due to the exchange ratio between the
two goods.
Calculate numerical substitution and income effects in consumption of good 1:
Assume that Tom maximizes his utility subject to the budget constraint P1X1+P2X2=m
x1= (20p1-3)/m p1=10 m=32.8
P1 goes from 10 to 7
What type of good is x1?
Taken from test 1 - 1. Find the demand of x1 by plugging in all of your data into x1.
This is our point A, original point (think about the graph that we usually do) 6.006
2. Find the compensation income (holds real income constant) so we can find the
substitution effect. This is measured by the change in price * the demand (function)
(new-old price)
a. (7-10)*6.006= -18.018 (this is the amount less needed to consume the same amount)
b. combine with original income
32.8-18.018= $14.782
3. We now use the new price and the compensated income so we can isolate the
effects of this new price change. Input the new stuff into the demand function.
20(7) -3/ 14.782 = 9.268 consumed at new price income held constant
4. Find the amount consumed with an income change.
20(7)-3/32.8 = 4.176
we have isolated the effect of the change in price in how much we are consuming.
Remember, we just want the price change because income effect is determined by the
, change in purchasing power from price change, not actual income change.... income
doesn't actually change, we just used the compensated income, which is hypothetical.
5. Find the actual effects, which are the changes in consumption from each effect.
9.268-4.176=5.092 income effect*** not sure if the order matters when finding the
difference here
9.268-6.006=3.259 substitution effect
x1 is a normal good because as income goes up (purchasing power) consumption also
increases. Also ordinary because when price goes down, consumption of good 1
increases.
Utility function is U(x1, x2)= x1+ x2 ^1/2
x1 price is $1, price x2 p2
1a Find demand functions for x1 and x2 using Lagrangian.
1b Is more spent on x1 or x2?
1c assume income m=5 p2= .5
find quantities demanded of x1 and x2
1d find income elasticity of demand for x1 and x2
Taken from exam 1 - 1. Set up the equation
L= x1+ x2 ^ 1/2 + Lambda(m-x1- x2p2)
2. Solve for the 3 partial derivative equations with respect to x1, x2, and lambda. Move
lambda to replace 0 too.
3. Find the Marginal Rate of Substitution (the rate @ which you exchange consumption
of one good for another)
format is (x1/x2) = (p1/p2) I remember it being that we typically do partial derivative of
x1 before x2, so it's already on top of the other one, which is how we use it in the ratio.
1/(1/2 *x2 ^-1/2) =(1lambda/lambdap2)
I moved the x2^1/2 up because of the negative exponent, make it easier to see things:
x2^1/2/.5 =1/p2
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