Topic 3 - Budget Constraints

(Lecture 2 Sept 21st)

Intuition:

1. Goods: x1, x2;

2. Price: p1, p2

3. E: total expenditure/budget the individual has;

Assume that all of E is spent, E = p1x1 + p2x2

Y-intercepts:

= maximum units of x2 that can be consumed;

Slope:

= OC = Units of x2 that have to be reduced to consume one more unit of x1;

-- Change in Variables:

x2 x2 x2

x1 x1 x1

E shifts outward p1 steeper p2 flatter

-- Non-linear Constraint budget x2

Liner budget constraint = assumption that prices are fixed;

In the real world, there might be non-linearity of prices

e.g. price of electricity depends on usage

x1<a, p1;

x1>a,2p1;

x2,p2 a x1

Inter- temporal Budget Constraint

Assume Y1,Y2 “income” in two periods;

x1p1 + x2p2 = Y1+Y2 x1 =

Suppose individual has initial asset = Ao

1. A1 (at the end of period 1) = Ao (1+r1) + Y1 – p1x1

2. A2 (at the end of period 2) = A1 (1+r2) + Y2 – p2x2

Suppose assume A2 = 0 “no bequest” case (spend everything you have)

From 2 A1 =

Plug back in 1

DPV of Consumption DPV of Assets + income

Solve:

Y-Intercept: FV of Consumption if Consumption in period 1 is 0;

Slope: OC of consumption in period 1 in terms of period 2

(How much consumption in period 2 has to be reduced to increase consumption in period 1)

Simplify:

Ao = 0; r1=r2; p1=p2=1;

X2 = The OC depends on the interest rate;

If the individual cannot borrow, the max he/she can consume is the income today (Y1 only).

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###### Document Summary

Topic 3 - budget constraints (lecture 2 sept 21st: goods: x1, x2, price: p1, p2, e: total expenditure/budget the individual has; Assume that all of e is spent, e = p1x1 + p2x2 . = maximum units of x2 that can be consumed; = oc = units of x2 that have to be reduced to consume one more unit of x1; - change in variables: x2 x2 x2 x1 x1 x1. Liner budget constraint = assumption that prices are fixed; In the real world, there might be non-linearity of prices e. g. price of electricity depends on usage x1<a, p1; x1>a,2p1; x2,p2 a x1. Inter- temporal budget constraint x1p1 + x2p2 = y1+y2 x1 = Suppose individual has initial asset = ao: a1 (at the end of period 1) = ao (1+r1) + y1 p1x1, a2 (at the end of period 2) = a1 (1+r2) + y2 p2x2. Suppose assume a2 = 0 no bequest case (spend everything you have)

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