PPA 723: Managerial Economics
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Transcript of PPA 723: Managerial Economics
PPA 723: Managerial Economics
Lecture 6:
Household Budget Constraints
Managerial Economics, Lecture 6: Budget Constraints
Outline
Household Budget Constraints
Price Indexes
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
Budget Constraint
QA
Opportunity set
Y/PB
Y /PA
QB
Infeasible set
Slope = -PB/PA
Managerial Economics, Lecture 6: Budget Constraints
Interpretation
A intercept = maximum possible amount of A
B intercept = maximum possible amount of B
= interceptA
YA
P
= interceptB
YB
P
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
Figure 4.7a Changes in the Budget Constraint
B, Burritosper semester
(a) Price of Pizza Doubles
Loss
50
L1 (pZ = $1)
L2 (pZ = $2)
25
250
Z, Pizzas per semester
Managerial Economics, Lecture 6: Budget Constraints
Figure 4.7b Changes in the Budget Constraint
B, Burritosper semester
(b) Income Doubles
Gain
100
L3 (Y = $100)
L1 (Y = $50)
50
25
500
Z, Pizzas per semester
Managerial Economics, Lecture 6: Budget Constraints
Changes in the Budget Constraint—Case c
B, Burritosper semester
(c) Free Pizza
Gain
100
L 4 (Y = $50, 50 Free Pizzas)
L1 (Y = $50)
50
25
500
Z, Pizzas per semester
Managerial Economics, Lecture 6: Budget Constraints
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!!!
Managerial Economics, Lecture 6: Budget Constraints
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.
Managerial Economics, Lecture 6: Budget Constraints
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.
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
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
Managerial Economics, Lecture 6: Budget Constraints
Extensions
Changing the base year
The index number problem
Which price index to use