Chapter 2 BUDGET CONSTRAINT

2.1 The Budget Constraint Consumers choose the BEST bundle of goods they can AFFORD. Budget set: affordability Consumption bundle: (x 1, x 2 )

2.1 The Budget Constraint The budget constraint p 1 x 1 +p 2 x 2 ≤m p 1 x 1 : the amount of money the consumer is spending on good 1. p 2 x 2 : the amount of money the consumer is spending on good 2. m: the consumer’s income

2.2 Two Goods Are Often Enough Composite good good 2 represents a composite good that stands for everything else that the consumer might want to consume other than good 1. The budget constraint will take the form: p 1 x 1 +x 2 ≤m

2.3 Properties of the Budget Set p 1 x 1 + p 2 x 2 = m p 1 (x 1 +Δx 1 ) + p 2 (x 2 +Δx 2 ) = m Subtracting the first equation from the second: p 1 Δx 1 + p 2 Δx 2 = 0 Δx 2 /Δx 1 =-p 1 /p 2

2.3 Properties of the Budget Set Opportunity cost of consuming good 1  the slope of the budget line.  In order to consume more of good 1 one has to give up some consumption of good 2.

2.4 How the Budget Line Changes Changes in income: a parallel shift of the budget line.

2.4 How the Budget Line Changes Changes in prices: increasing price 1 while holding price 2 and income fixed.

2.4 How the Budget Line Changes Change the price of good 1 and good 2 at the same time: Multiplying both prices by t yields tp 1 x 1 +tp 2 x 2 = m p 1 x 1 +p 2 x 2 = m/t

2.5 The Numeraire The budget line p 1 x 1 + p 2 x 2 = m is exactly the same budget line as p 1 / p 2 x 1 + x 2 = m/p 2 or p 1 / mx 1 + p 2 / mx 2 = 1

2.6 Taxes, Subsidies, and Rationing Quantity tax  t dollars per unit of good 1,  changes the price of good 1 from p 1 to p 1 +t. Quantity subsidy  s dollars per unit of good 1,  the price of good 1 would be p 1 -s.

2.6 Taxes, Subsidies, and Rationing Value tax  a sales tax at rate t,  the actual price is (1+t)p 1. Ad valorem subsidy  an ad valorem subsidy at rate s,  the actual price is (1-s)p 1.

2.6 Taxes, Subsidies, and Rationing Lump-sum tax the budget line shifts inward. Lump-sum subsidy the budget line will shift outward.

2.6 Taxes, Subsidies, and Rationing Rationing Good 1 rationed.

2.6 Taxes, Subsidies, and Rationing Sometimes taxes, subsidies, and rationing are combined.