1) Choice and Constraints on Choice Budget set … Feasible

Consumption Choice Sets Collection of all consumption choices available to the consumer Constraints consumption choice

o Budgetary, time and other resource limitations

Budget Constraints Consumption bundle:

o x1 units of commodity 1

o x2 units of commodity 2 …

o xn units of commodity n

denoted by vector (x1, ... , xn) commodity prices p1,p2 … pn when is a consumption bundle (x1, ... , xn) affordable at prices p1,…,pn?

o when don’t cost any more than mp1x1 + … + pnxn < m

m consumer’s disposable income budget constraint: (budget line)

the bundles that are just affordable budget constrainto bundles ON the constraint

consumer’s budget set is set of all affordable bundles

o budget constraint is upper boundary of the budget set composite good: everything else consumer might want to consume other than good 1

Budget Set and Constraint for Two Goods budget line slope = -p1/p2

change in x2/change in x1 = -p1/p2 budget line measure opportunity cost of consuming good 1

Budget Constraints

Budget Constraint for Three Commodities Budget Set for Three Commodities

Budget Sets & constraints; Income and Price Changes budget constraint and set depends on prices and income when one changes

Budget set change: Income m increases gives more choice

Budget set change: Income m decreases

Budget Constraints - Income Changes Increases in income m

o shift constraint outward in parallel enlarging budget set improving choiceo original choice isn’t lost, new choices addedo cant make consumer worse off

decreases in income m o shift constraint inward in parallel shrinking budget set reducing choiceo may make consumer worse off

Budget Constraints – Price Changes if just one price decreases? From P1’ to P1’’

reducing price of one commodity pivots the constraint outwardo cant make consumer worse off

increasing one also pivots inward make consumers worse off

Uniform Ad Valorem Sales Taxes Ad valorem sales tax levied at a rate of 5% p (1 + 0.05)p = 1.05p Levied at a rate of t increases all prices by tp from p (1 + t)p Uniform sales tax: applied uniformly to all commodities

o Levied at rate t changes constraint

Subsidy quantity subsidy gov’t gives an amount to consumer that depends on that amount of good

purchasedo if consumption of milk subsidized gov’t pay some amount to each milk consumer

depending on amount purchased (p1 – s)o budget line = flatter

ad valorem subsidy price of good one with ad valorem subsidy = vo (1 – v) p1

Lump Sum lump sum tax gov’t takes away some fixed amount of money budget line = shift inward (income reduced) lump sum subsidy budget line = shift outward

Rationing level of consumption is fixed to be no larger than some amount

The Food Stamp Program taxes, subsidies and rationing combined coupons that can be legally exchanged only for food how does it alter a family’s budget constraint?

o M = $100o Pf = $1o Price of other goods Pg = $1o Budget constraint F + G = 100

What if food stamps can be traded on black market for $.50 each?

Budget Constraint – Relative Price Numeraire = unit of account Rearrange budget line :

o OR o first case p2 =1 m =1

doesn’t change budget set at allo when we set one of the prices to 1 numeraire price

price relative to which we are measuring other price and income prices and income measured in dollars

o p1 = $2, p2 = $3, m = $12o constraint 2x1 + 3x2 = 12

prices and incomes measured in centso p1 = 200, p2 = 300, m = 1200o constraint 200x1 + 300x2 = 1200 (same as $)

changing numeraire changes nothing constraint 2x1 + 3x2 = 12

o 1*x1 + (3/2)x2 = 6o constraint for p1 = 1, p2 = 3/2, m = 6o p1 = 1 makes Commodity 1 the numeraire and defines all prices relative to p1;

3/2 is price of commodity 2 relative to price of commodity 1 any commodity can be chosen as numeraire without changing the budget set/constraint p1 = 2, p2 = 3 & p3 = 6

o price of commodity 2 relative to 1 is 3/2o price of commodity 3 relative to 1 is 3o relative prices are the rates of exchange of commodities 2 and 3 for units of commodity

1

Shapes of Budget Constraints what makes a budget constraint a straight line?

o A straight line constant slope and constraint:

o If prices are constant constraint is a STRAIGHT line If prices not constants?

o (bulk buying discounts, price penalities)o constraint CURVED

Quantity Discounts p2 constant at $1 p1 = $2 for 0 < x1 < 20 p1 = $1 for x1 > 20 constraints slope is

o

o constraint

Quantity Penalty

Application x1 is consumption ($) NOW, x2 is consumption in FUTURE consumer has income $m1 NOW, $m2 in FUTURE can lend at interest rate rL but must pay rH (>rL) to borrow intertemporal (over time) budget

One price Negative commodity 1= stinky garbage paid $2 per unit to accept it income outside of collecting garbage is m = $10

o constrainto -2x1 + x2 = 10 OR x2 = 2x1 + 10

More General Choice Sets choices constrained by more than a budget

o time constraints and other resource constraint bundle only available if it meets every constraint

choice set is the intersection of all the constraint sets