Budget Constraint - Handout 1

Simona Montagnana1

I.INTRODUCTION all his/her money of good 1, M . Then ask yourself how p1 In this handout we describe briefly the budget constraint, much of good 2 the consumer could buy if he/she spent all his/her money of good 2, M . which represents the consumer’s income: the amount of p2 money the consumer spends for a consumption’s bundle (x1,x2) at the respective prices (p1, p2). We give some exam- ples of budget constraint created by rationing, promotional coupon, etc... X2

II.BUDGET CONSTRAINT

M/p2 A consumption bundle (x1,x2) is a combination of quan- tities of the various goods (services) that are available to be Budget line M= 푝1푥1 + 푝2푥2 consumed. A consumer prefers some consumption bundles to others, but he/she has a budget constraint and cannot spend more money (income) than he/she has. 푝 Slope =− 1 The budget set is a set of all bundles that satisfy the budget 푝2 Budget set constraint, given a set of prices (p1, p2) and the income M.

p1x1 + p2x2 ≤ M M/p1 X1 The budget line is the set of bundles for which the consumer is spending exactly what he/she has. Fig. 1. Budget set p1x1 + p2x2 = M If we rearrange the budget line, we get its slope: III.BUDGETLINECHANGES M p1 x = − x When prices (p ; p ) or income (M) change the set of 2 p p 1 1 2 2 2 goods that a consumer can afford changes as well and the From which we get that the slope of the budget line is: budget line and / or his slope may change. p − 1 p2

This is the amount of ∆x2 of good 2 that the consumer X2 must give up if he/she wants to consume an additional M’/p2 amount ∆x of good 1. The slope of the budget line 1 M/p defines the cost opportunity (trade off) for the consumer 2 Budget line 푀 = 푝1푥1 + 푝2푥2 who wants to increase his/her consumption of good 1 and ′ simultaneously decrease his/her consumption of good 2. New Budget line 푀 = 푝1푥1 + 푝2푥2 This means that the total value of the change in his /her 푝 Slope =− 1 consumption must be zero. 푝2

p1(x1 + ∆x1) + p2(x2 + ∆x2) = M

p1∆x1 + p2∆x2 = 0 M/p1 M’/p1 X1 ∆x p 2 = − 1 ∆x1 p2 In order to know the budget line intercepts, just ask yourself Fig. 2. Increasing Income how much of good 1 the consumer could buy if he/she spent

1 Department of Economics, University of Bath - England s.montagnana at bath.ac.uk X2 X2

M/p2 M/p2

Budget line 푀 = 푝1푥1 + 푝2푥2 Budget line 푚 = 푝1푥1 + 푝2푥2

′ New Budget line 푀 = 푝1푥1 + 푝2푥2 푝 Slope =− 1 푝2

푝′ ′ New Slope =− 1 푝1 푝1 푝1+푡 푝 Slope =− New Slope =− = − 2 푝2 푝2 푝2

M/p1’ M/p1 X1 X X1

Fig. 3. Increasing price of good 1 Fig. 6. A 2-for1 Store coupon / Taxing consumption

X2

X2

M/p2’

M/p2 M/p2

Budget line 푀 = 푝1푥1 + 푝2푥2 Budget line 푚 = 푝1푥1 + 푝2푥2 푝 Slope =− 1 푝 2 푝 Slope =− 1 푝2

푝1 ′ New Slope =− ′ New Budget line 푀 = 푝1 푥1 + 푝2푥2 푝2

0 M/p M/p1 X1 X 1 X1

Fig. 4. Decreasing price of good 2 Fig. 7. Coupons

IV. ODD BUDGETCONSTRAINTS REFERENCES [1] Varian H. (2017) Intermediate Microeconomics, 9th ed. [2] Serrano R and A. M. Feldman, (2013), Intermediate Microeconomics with calculus, 2nd ed. Cambridge.

X2

M/p2

Budget line 푚 = 푝1푥1 + 푝2푥2

푝 Slope =− 1 푝2

X X1

Fig. 5. Rationing