Chapter 2 BUDGET CONSTRAINT 2 1 The Budget

Chapter 2 BUDGET CONSTRAINT

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

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

2. 2 Two Goods Are Often Enough n Composite good 2 represents a composite good that stands for everything else that the consumer might want to consume other than good 1. n 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 n Subtracting the first equation from the second: p 1Δx 1 + p 2Δx 2 = 0 Δx 2/Δx 1=-p 1/p 2

2. 3 Properties of the Budget Set n 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. x 2 m/p 2 -p 1/p 2 m/p 1 x 1

2. 4 How the Budget Line Changes x 2 n Changes in income: a parallel shift of the budget line. m’/p 2 m/p 2 -p 1/p 2 m/p 1 m’/p 1 x 1

2. 4 How the Budget Line Changes n Changes in prices: increasing price 1 while holding price 2 and income fixed. x 2 m/ p 2 -p 1/ p 2 m/ p 1’ m/ p 1 x 1

2. 4 How the Budget Line Changes n 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 n 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 n Quantity tax ¨t dollars per unit of good 1, ¨ changes the price of good 1 from p 1 to p 1+t. n 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 n Value tax ¨a sales tax at rate t, ¨ the actual price is (1+t)p 1. n Ad valorem subsidy ¨ an ad valorem subsidy at rate s, ¨ the actual price is (1 -s)p 1.

2. 6 Taxes, Subsidies, and Rationing n Lump-sum tax the budget line shifts inward. n Lump-sum subsidy the budget line will shift outward.

2. 6 Taxes, Subsidies, and Rationing n Rationing x 2 Good 1 rationed. Budget line Budget set x 1

2. 6 Taxes, Subsidies, and Rationing n Sometimes taxes, subsidies, and rationing are combined. x 2 -p 1/p 2 -(p 1+t)/p 2 x 1