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.

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:

Managerial Economics, Lecture 6: Budget Constraints  To express a budget constraint in this form,  Step 1: Switch sides:  Step 2: Subtract P B Q B from both sides  Step 3: Divide both sides by P A

Managerial Economics, Lecture 6: Budget Constraints Budget Constraint QAQA Opportunity set Y / P B Y / P A QBQB Infeasible set Slope = -P B /P A

Managerial Economics, Lecture 6: Budget Constraints Interpretation  A intercept = maximum possible amount of A  B intercept = maximum possible amount of B

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 P A of income.  $1 of income buys 1/ P B units of B.  So giving up one unit of A allows the household to buy P A /P B units of B (the run).  Hence, the rise over the run (the slope!) is - P B /P A.

Managerial Economics, Lecture 6: Budget Constraints Budget Constraint (from Textbook)  Lisa spends all her income, Y, on pizza and burritos  Her budget constraint is  p B B = expenditure on B (burritos)  p z Z = expenditure on Z (pizzas)

Managerial Economics, Lecture 6: Budget Constraints Figure 4.6 Budget Constraint B, Burritos per semester Opportunity set 50= Y/p Z L 1 (p Z = $1,Y = $50) 25 = Y/p B 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:

Managerial Economics, Lecture 6: Budget Constraints Figure 4.7a Changes in the Budget Constraint B, Burritos per semester (a) Price of Pizza Doubles Loss 50 L 1 (p Z = $1) L 2 (p Z = $2) 25 0 Z, Pizzas per semester

Managerial Economics, Lecture 6: Budget Constraints Figure 4.7b Changes in the Budget Constraint B, Burritos per semester (b) Income Doubles Gain 100 L 3 (Y = $100) L 1 (Y = $50) Z, Pizzas per semester

Managerial Economics, Lecture 6: Budget Constraints Changes in the Budget Constraint—Case c B, Burritos per semester (c) Free Pizza Gain 100 L 4 (Y = $50, 50 Free Pizzas) L 1 (Y = $50) 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 :

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  All price indexes have a base year.  The 100 is just for convenience.

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

Managerial Economics, Lecture 6: Budget Constraints Extensions  Changing the base year  The index number problem  Which price index to use