PPA 723: Managerial Economics Lecture 6: Household Budget Constraints

PPA 723: Managerial Economics

Lecture 6:

Household Budget Constraints

Managerial Economics, Lecture 6: Budget Constraints

Outline

Household Budget Constraints

Price Indexes


The Household Budget Constraint

A household budget constraint sets income equal to spending

We do not consider savings or borrowing, but the analysis could be extended to them.

A A B BY P Q P Q


Graphing the Budget Constraint

In this equation, the Q’s are variables, Y and the P’s are fixed constants.

The usual forms for a line with variables x (horizontal axis) and y (vertical axis) are:

= + , where = intercept and = slopey a bx a b

= + , where = intercept and = slopey mx b b m


To express a budget constraint in this form,

Step 1: Switch sides:

Step 2: Subtract PBQB from both sides

Step 3: Divide both sides by PA

+ = A A B BP Q P Q Y

= A A B BP Q Y P Q

= BA B

A A

PYQ Q

P P


Budget Constraint

QA

Opportunity set

Y/PB

Y /PA

QB

Infeasible set

Slope = -PB/PA


Interpretation

A intercept = maximum possible amount of A

B intercept = maximum possible amount of B

= interceptA

YA

P

= interceptB

YB

P


Slope = trade-off between the two goods:

Slope shows units of A one can obtain by giving up a unit of B at market prices: If a household gives up one unit of A (the rise is -1), it

frees up PA of income.$1 of income buys 1/PB units of B.So giving up one unit of A allows the household to buy

PA/PB units of B (the run).Hence, the rise over the run (the slope!) is -PB/PA.

= slopeB

A

P

P


Budget Constraint (from Textbook)

Lisa spends all her income, Y, on pizza and burritos

Her budget constraint is

pB B = expenditure on B (burritos)

pz Z = expenditure on Z (pizzas)

B Zp B p Z Y


Figure 4.6 Budget Constraint

B, Burritosper semester

Opportunity set

50 = Y/pZ

L1 (pZ = $1, Y = $50)

25 = Y/pB

20

10

100 30

Z, Pizzas per semester

a

b

c

d


Slope of Budget Constraint, Cont.

Textbook calls the slope the marginal rate of transformation

In the book’s example:

Z

B

B pMRT

Z p

$1 1

$2 2Z

B

pMRT

p


Figure 4.7a Changes in the Budget Constraint


(a) Price of Pizza Doubles

Loss

50

L1 (pZ = $1)

L2 (pZ = $2)

25

250



Figure 4.7b Changes in the Budget Constraint


(b) Income Doubles

Gain

100

L3 (Y = $100)

L1 (Y = $50)

50

25

500



Changes in the Budget Constraint—Case c


(c) Free Pizza

Gain

100

L 4 (Y = $50, 50 Free Pizzas)

L1 (Y = $50)

50

25

500



Inflation

Inflation is a general rise in prices.

It affects commodity prices and input prices, such as wages.

What happens to the budget constraint if income and prices increase by the same percentage?

Answer: Nothing!!!


General inflation therefore has no effect on real opportunities.

Inflation may still have real consequences:Inflation tends to increase uncertainty and

thereby lower investment and slow growth.In some cases inflation can help promote a

country’s trade – and hence its economic development.

Inflation redistributes toward those who anticipated it or are insured against it.


Price Indexes

Although general inflation does not shift the budget constraint, income and prices do not always move together.

So how can one compare possibilities for consumption in two different years?

Answer: Construct a price index, and use it to calculate real income.


Start with consumption by a typical household (quantity for each of N goods and services), called a market basket.

Figure out how much it costs to buy this market basket at the prices in year t :

1 1 2 2 = ... t t t Nt NS P Q P Q P Q


A price index is the amount a household must spend for the market basket in year t relative to some (arbitrary) base year, say 2000.

All price indexes have a base year.

The 100 is just for convenience.

2000

= 100 tt

SI

S


To translate a dollar variable between nominal and real terms, divide by the price index:

Example: Nominal income is $30,000 in 2010 and $20,000 in 2000. The price index (with a 2000 base) is 150 in 210. So real income (in 2000 dollars) is $20,000 in both years.

NominalReal =

Price Index/100

CurrentConstant =

Price Index/100


Extensions

Changing the base year

The index number problem

Which price index to use

Documents

PPA 723: Managerial Economics Lecture 6: Household Budget Constraints