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Economics 202: Intermediate Microeconomic Theory - PowerPoint PPT Presentation

Economics 202: Intermediate Microeconomic Theory. 1. Student Information Sheets 2. Any questions? 3. For next time, finish reading Chapter 5 4. HW #2 due Thursday in class (it’s on the website). Budget Constraints. Shifts in the Budget Line Change in Income Change in Prices

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Economics 202: Intermediate Microeconomic Theory

1. Student Information Sheets

2. Any questions?

3. For next time, finish reading Chapter 5

4. HW #2 due Thursday in class (it’s on the website)

• Shifts in the Budget Line

• Change in Income

• Change in Prices

• Double I, Triple PX & PY?

Yo-yos

I/PY

2I/3PY

• NB: slope measures the real price, the purchasing power of one good in terms of the other

• so if both prices rise by the same % (or fall by same %), their ratio is the same  the slope of budget line stays same!

• Composite consumption good x2: p1x1 + 1x2 = m

• What if the price changes with quantity purchased?

2I/3PX

I/PX

Xylophones

• Change in Income

• lump-sum tax or subsidy (grant)

• “earmarked” grant

• Change in Prices

• Per-unit tax or subsidy (quantity tax or subsidy)

• Ad valorem tax or subsidy (value/proportional tax or subsidy)

• Two criteria:

(1) slope of IC = slope of budget line

(2) we have to be on the budget line

• This will give us 2 equations in 2 unknowns, and we can solve for optimal values

• General Lagrangian & MRS = PX/PY is only a necessary condition for utility maximization. Assumption of dim. MRS (strict convexity) gives sufficiency for utility maximization.

• U = GT Income = \$100 Ptennis racquet = \$10

• What is Roger’s optimal consumption bundle of Gatorade and tennis racquets?

• Three approaches

• Approach #1

• Write down & solve the MRS condition and budget constraint

• Approach #2

• Create unconstrained utility maximization problem

• Approach #3

• Constrained utility maximization problem (use the Lagrangian)

•  has an economic interpretation

• Check 

• Let I = \$101 and calculate the resulting increase in utility …

• We had U = GT, I = \$100, PG = \$5 per bottle, PT = \$10 per racquet

• This gave us G* = 10 bottles, T* = 5 tennis racuets for U* = 50 “utils”

a

U2

U1

U0

Final four tickets

Exception: Corner Solution

• At point “a”, MRS < slope of the budget line

• But that is our final point since we can’t consume less than 0 Final Four tickets

• NB: the optimality condition (MRS = slope of budget line) only holds for cases in which we consume positive amounts of BOTH goods.

• FOC’s must be modified with a  sign, rather than = sign.

• When, e.g., U/X - PX < 0, then X* = 0.

• PX > MUX /  which says ?

• Derive the demand functions for the quasi-linear function

U(X,Y) = ln X + Y

X* = dX(PX, PY, I; tastes) Y* = dY(PX, PY, I; tastes)

• Green is a foreshadowing to emphasize now that this is Marshallian demand (uncompensated demand) which holds income fixed.

Numerical example:

U = ln X + Y Income = \$10 PX = PY = \$1

• Are these homothetic preferences?

• What is optimal consumption bundle (X*,Y*)?

• What is utility at the optimum?

• What is the marginal utility of income at the optimum?