Economics 202 intermediate microeconomic theory
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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). Budget Constraints. Shifts in the Budget Line Change in Income Change in Prices

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Economics 202: Intermediate Microeconomic Theory

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Economics 202 intermediate microeconomic theory

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)


Economics 202 intermediate microeconomic theory

Budget Constraints

  • 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


Economics 202 intermediate microeconomic theory

Budget Constraints

  • 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)


Optimal consumption

Optimal Consumption

  • 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

    Pgatorade = $5

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

  • Three approaches


Optimal consumption1

Optimal Consumption

  • 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”


Economics 202 intermediate microeconomic theory

Pretzels

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 ?


Optimal consumption2

Optimal Consumption

  • 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 + YIncome = $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?


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