Consumer Theory II Flashcards
What does the Utility Function, U(x, y), imply?
It implies the Consumer only cares about Goods x and y, nothing else
-Both Goods must be consumed to gain Utility
Denote the Price of x + the Price of y
Price of x = Px
Price of y = Py
What is the Budget Constraint equation?
Budget = Px(x) + Py(y)
What is the MRS and how do you calculate it?
MRS- Marginal Rate of Substitution shows the Slope of the Indifference Curve
MRS = dy/dx
At the Optimum Consumption Bundle, what is the Slope of the Budget Constraint equal to?
MRS
how do you find the optimum level of Consumption for goods x and y?
Find the Slope of the Budget Constrain (B.C)-
—dU = ydx + xdy = 0
Equate MRS and Slope of B.C, MRS = Slope
Rearrange in terms of y and Sub. back into B.C
What does Marginal Utility tell us?
It tells us What the Gain in Utility is if we Increased Consumption of the Good by a small amount
What happens to Utility if you change the amount of each Good you Consume?
You can Consume different amounts of the Goods, BUT you Stay on the SAME Indifference Curve
So, Change in Utility, dU, is 0
What do you use to find the Total Change in Utility?
Partial + Total Derivatives
What does [dU(x, y) / dx] x dx show?
dU if x changes (a little), keeping y constant
Marginal Utility of x
What does [dU(x, y) / dy] x dy show?
dU if y changes (a little), keeping x constant
Marginal Utility of y
What is the Equation for the Total Change in Utility?
dU(x, y) = Marginal Utility of x dx + Marginal Utility of y dy
dU(x, y) = [dU(x, y) / dx] x dx + [dU(x, y) / dy] x dy
dU(x, y) = MUx dx + MUy dy
Given that you remain on the same Ic, show that the Change in Utility = -MUx/MUy
dU(x, y) = MUx dx + MUy dy If you remain on same Ic--> Change in Utility = 0 => dU(x, y) = 0=> 0 = MUx dx + MUy dy =>MUx dx = -MUy dy dy/dx = MRS = -MUx/MUy
If Income Increases, what happens to the Ic for a Normal Good?
B.C + Ic Shift Outwards- to the Right
Can Consume more of Both Goods
If Income Increases, what happens to the Consumption of an Inferior Good?
B.C Shifts Outwards- to the Right
Ic Shifts Left- But is on NEW B.C
—Consume less of Good x (Inferior Good)
Consume more of y and less of x
What are the 2 effects on the Law of Demand?
Income + Substitution effects
What happens to the B.C if the Price of Good x falls?
B.C rotates about Py- M/Px moves along x axis
What does a Change in the Price of a Good cause?
Change in Choice of Consumption
What does Px/Py show?
How expensive Good x is relative to Good y
Tells us our Incentive to Substitute x for y- e.g. Increase x + Decrease y
What does M/Px tell us?
Tells us Income in REAL Terms of Good x
-Shows how our Income Changes
Fall in Price of Good x–> Increase REAL Income in terms of Good x
How does a fall in the Price of x of a Normal Good affect the B.C + Ic? Explain effects of Income + Substitution effects
Fall in Price of x–> M/Px moves along x axis
Intermediate Step: Line Tangent to Ic1 but parallel to B.C2
–Where this line is a Tangent to Ic1- shows Consumption after impact of Substitution effect
Where B.C2 is tangent to Ic2- shows final Consumption + Income effect from Intermediate Step
What does the Substitution effect depend on?
Depends ONLY on Price Change
What does the Income effect depend on?
Depends ONLY on fact REAL Income Increases
For an Inferior Good, which out of the Substitution + Income effects is Positive + Negative?
Substitution- POSITIVE
Income- Negative
