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
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)

slide2
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

slide3
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”
slide6
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 + 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?
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