ECOS2001 STUDY GUIDE

BUDGET CONSTRAINT, PREFERENCES, MARGINAL RATE OF SUBSTITUTION Week 1; Chapters 2 & 3 Chapter 2 Budget constraints • Consumption bundle indicated by (x1, x2)

• Tells us how much the consumer is choosing to consume of good 1 (x1) and good 2 (x2)• Budget constraint:

• Where m is income and p1 and p2 are prices• Budget set: affordable consumption bundles that don’t cost more than m• Can think of good 2 as the dollars the consumer uses to spend on other goods

• Amount of money spent on good 1 + amount of money spent on all other goods must be ≤ m

• Good 2 represents a composite good• Budget line: set of bundles that cost exactly m

• Bundles of goods that just exhaust the consumer’s income

• Slope of budget line: rate at which the market is willing to “substitute” good 1 for good 2• If consumption of good 1 increases, how much will consumption of good 2 have to

change to satisfy her budget constraint?• Opportunity cost of consuming a good

Changes in the budget line • Increase in income Ⱦ parallel shift outward of the budget line

• Slope stays same

• Increasing price of good 1 (x axis) Ⱦ budget line becomes steeper• If p2 increases more than p1 (-p1/p2 decreases in absolute value) Ⱦ budget line becomes

flatter

• Sales tax t on both goods is equivalent to income tax of

• Rationing constraints: level of consumption of some good is fixed to be no larger than some amount• Eg. WWII US government rationed certain foods• Budget set would be the same with a piece lopped off

• Lopped-off piece consists of consumption bundles that are affordable but have x1 > rationed amount (x̄1)

• Combination of taxing and rationing• Taxing consumption greater than x̄1

• Eg. Food stamps• Pre-1979: Ad valorem subsidy on food (rate was based on household income)• Post-1979: Food stamps were given to qualified households

Chapter 3 Preferences • Preference is based on consumer’s behaviour• Consumption bundles: objects of consumer choice/complete list of goods and services involved

in the choice problem• Bundle (x1, x2) can be ranked differently to (y1, y2)

• Strictly preferred• (x1, x2) strictly preferred to (y1, y2)

• Weakly preferred• (x1, x2) weakly preferred to (y1, y2)

• Cobb-Douglas preferences• Optimal choices are

Choosing taxes • Quantity tax: tax on amount consumed of a good (eg. Gasoline tax of 15 cents per gallon)• Income tax: tax on income • Should government raise revenue via quantity tax or income tax?

• Quantity tax (tax consumption of good 1 at a rate of t)• Similar to raising price of good 1 by t

• Revenue raised by this tax is R* = tx1*• Income tax that raises same amount of revenue

• Income tax is superior to quantity tax (can raise same amount of tax revenue but have the sole consumer be better off under income tax)

Chapter 6 Demand • Demand functions give optimal amounts of each of the goods as a function of prices and

income

• Comparative statics: studying how a choice responds to changes in economic environment

Normal and inferior goods • Normal goods: demand increases when income increases • Inferior goods: demand decreases when income increases

Pareto efficient allocations • Allocation is Pareto efficient when there are no exchanges that are advantageous for both

parties • No way to make all people better off • No way to make an individual better off without making the other worse off • All gains from trade have been exhausted • No mutually advantageous trades • Set of bundles that A prefers does not intersect with set of bundles that B prefers

• Pareto set/contract curve: set of all Pareto efficient points in the Edgeworth box Market trade • Gross demands: amounts a person wants to consume • Net demands/excess demands: amounts a person wants to purchase

• Excess demand of agent A for good 1: • If there is excess demand for one of the goods, auctioneer will raise the price and vice versa if

there is excess supply • Until demand = supply

• Market equilibrium/competitive equilibrium/Walrasian equilibrium: set of prices such that each consumer is choosing his/her most-preferred affordable bundle, and all consumers’ choices are compatible (ie. demand = supply in every market)

• Marginal rate of substitution will be the ratio of the prices • Equilibrium at (p1*, p2*)

• Equilibrium in Edgeworth box:

• Eg. A might choose to play Top 50% of the time and Bottom 50% of the time, B might choose to play Left 50% of the time and Right 50% of the time

• Probability of ¼ of ending up in each of the four cells in the matrix • Average payoff for A will be 0 and average payoff for B will be ½

• Nash equilibrium in mixed strategies: equilibrium in which each agent chooses the optimal frequency with which to play his strategies given the frequency choices of the other agent

• Nash equilibrium always exists in mixed strategies Prisoner’s dilemma Repeated games • With repeated games, defecting in one round can lead to a punishment in the next round

• Players have opportunity to establish reputation for cooperation • Viability of this strategy depends on whether game will be played a fixed or indefinite

number of times • With fixed games, players are likely to choose dominant strategy equilibrium and defect

in final round • If player defects in final round, there is no reason to cooperate in previous round • Player will defect on every round

• Cooperation requires that there will be a possibility of future play • With indefinite games, refusing to cooperate in one round can lead opponent to refuse to

cooperate in the next round • Winning strategy: tit for tat

• Cooperate if opponent cooperated in previous round • Defect if opponent defected on previous round

Sequential games • Payoff matrix of sequential game • Extensive form of the game