Chapter2 Budget Constraint

Chapter2 Budget Constraint

1. what if we increase all the price and income by t times? To change equilibrium, what should be done?
2. Revisit Fig.2.6 - For the allotment of $153 worth of food stamp, two cases of income level for household of 4 are given:
3. Income $300 -> pay $83 -> 83/153 is the new price for food
4. Income $100 -> pay $25

setting , the slope now becomes?

Chapter3 Preferences

1. Axioms
2. Completeness (include all cases of pref.),
3. Reflexivity (for own bundle),
4. Transitivity (logical consistency),
5. For well-bahaved preferences, followings are assumed
6. Monotinicity (the more, the better)
7. Convexity - averages are preferred to extremes
8. Local Nonsatiation (See Varian p.96)
9. Marginal rate of substitution (MRS) - marginal willingness to pay

Chapter4 Utility

1. Cardinal utility with monotonic transformation, ordinal utility
2. perfect substitute and complements
3. Quasilinear preferences - vertically shifted version of one indifference curve

1. Cobb-Douglas Utility function - what is the share of to income?
2. MRS and marginal utility - an empirical estimation

Taxation on Oil and Welfare

Test the Empirical Validity of an Economic Model

Energy Security and Taxation, Rebate Policy

"전기와 같은 공공재"?? - Public Good such as Electricity??

Chapter5 Choice

1. consumer choice
2. Gov't policy and utility using C-D utility function
3. taxation and welfare (income tax or tax on price, quantity tax)

Current bundle or new bundle after tax to be considered?

Q. CES utility function with budget constraint! Homework!

Chapter6 Demand

1. Why demand function is given such as ? Using C-D utility function to see the general form of demand function![1]
2. income change and the types of goods (normal, inferior, necessary vs. luxury)
3. income offer curve and Engel curve (M,) -> C-D case?
4. Homothetic function - consumer preferences depending only on the ratio of good 1 and 2. (see Varian p.18) - check the fact that income elasticity of demand equals 1.

1. Price change and the types of goods (ordinary, Giffen goods)
2. Price offer curve and demand function (substitute, complement)
3. Inverse demand function . =>

For any optimal level of , this implies Opportunity cost, Marginal Willingness to Pay!

Chapter7 Revealed Preference

1. Weak Axiom of Revealed Preference (WARP). If is directlyrevealed preferred to , and the two bundles are not the same, then itcannot happen that is directly revealed preferred to .
2. Strong Axiom of Revealed Preference (SARP). If is revealedpreferred to (either directly or indirectly) and is differentfrom , then cannot be directly or indirectly revealedpreferred to .
3. Check the violation of WARP, SARP using tables
4. Index Numbers for the comparison of base year and period
5. Laspeyres (base year)
6. quantity index (base year price) <1,
7. price index (base year quantity)
8. Paasche (period)
9. quantity index (base year price) >1,
10. price index (base year quantity)

Let and , what does it mean? better off in year b. Why?

If , better off in year t.

1. What happens to welfare with indexing the cost of living?

Chapter8 Slutsky Equation(For details, see Varian, p.120)

1. Decomposition of price effect into substitution effect, income effect
2. Revisit Giffen goods -
3. Energy Issues Related:
4. OPEC price hikes and energy security - what policy to adopt? only to reduce the dependence on foreign oil or and rebate?
5. RTP (Real Time Pricing) - Even if the RTP is introduced, baseline budget isguaranteed.
6. Compendated demand and Hicksian substitution effect

Curse of resources

Benefit Cost Analysis of Environmental Good

Depletable Resources and Forest Management

Gasoline Price and war profiteering

Chapter9 Buying and Selling

1. Price change with given endowment. Revisit Ricardian Trade model
2. immiserizing growth and oil (Machinery and Oil price and China) using Fig 9.3
3. What if ?
4. Endowment effect and Slutsky equation
5. Labor market - wage as opportunity cost of leisure (p.174)
6. Backward-bending labor suppy curve and Slutsky equation

1. Overtime payment and welfare

Chapter10 Intertemporal Choice

1. Consumption of vs. with given endowments of vs. for each time period of 1, and 2.
2. How to represent the budget line? How lender and borrower are different? (Compare this with Chapter 9.1.)
3. Slutsky equation revisited:
4. Inflation

setting =1, then . Let or real interest rate, it can be shown that

1. PV (Present Value), IRR, Bond and tax on interest payment

Chapter11 Asset Markets -> Risky Asset combined with Uncertainty (Chapter 13)

1. Interesting interpretation of equation representing NPV in terms of no arbitrage (11.1, 11.2)
2. Adjustment of differences in asset characteristics: liquidity, risk (Chapter 13), consumption return, tax, etc
3. Assets with consumption return - financial investment vs. buying consumption good: With high value of consumption return such as appreciation of the asset or high rental income, buying consumption good is a sensible choice to financial investment.
4. Assets with tax: Does capital gain tax neutral if it is the rate of ordinary income tax?
5. Capital gain tax is realized only when it is sold while dividend, interest payment is being paid every year.
6. Nominal asset value increase with no real value increase is also subject to taxation. Municipal bond with no Federal tax, own housing with no tax, etc. Adjustment will occur such as
7. Market Bubbles
8. Depletable Resources :
9. No arbitrage
10. What determines the price?or where , current oil price, , cost of alternative fuel
11. Forest Management

[2]

=> At optimal value of T, the rate of interest rate equals the rate of growth rate of the value of forest.

1. Gasoline Price and war profiteering?

Chapter12 Uncertainty (Individual behavior with uncertainty)

1. Initial Asset , loss with probability , insurance payment of with premium of , then

with ,

with ,

1. Current contingent consumption (endowment) and Contingent consumption plan with the purchase of insurance as a budget
2. or

From the above case,

From insurance companies point of view, profit P can be

for zero profit condition

1. Expected Utility Function or vonn Neumann-Morgenstern Utility Function
2. Risk Aversion, Risk Neutral and Risk Loving
3. With initial asset and the purchase of risk asset , how much is to be invested in risky asset? What if there is rate of tax for risky asset? What is the implication?

with ,

with ,

Tax reduces expected return but at the same time it reduces the risk. By scaling up the investment on risky asset by 1/(1-t) or , expected return could be exactly the same as before.

Chapter13 Risky Assets (Market with uncertainty)

1. For states , with each states have probability of , a random variable takes on the value , the the mean and variance of this prob. distribution are

1. Let us denote risk free rate of return , risky asset return of state s , average return on risky asset , holding fraction of and for risky asset and risk free asset, respectively. Then the expected return on your portfolio will be

1. Budget line of risk and return
2. Price of risk
3. as the riskiness of an asset relative to the risk of the market
4. risk adjustment and CAPM

1. Suppose in view of as expected value of

Chapter14 Consumer Surplus

1. Explanation using quasilinear utility function

If consumer is indifferent to consuming or not, the price is called reservation price.

At reservation price , consumer is indifferent to consuming units or units, then . If utility function is quasilinear , and ,

Q. Show if consumer demands units of good 1.

use

If consumer chooses n units of discrete good 1, his total utility is

where is consumer surplus.

1. Measurement of CS - errors from estimation of demand > approximation error
2. How to obtain monetary measures of utility
3. Compensating Variation (CV, The change of income necessary to restore original utility level),
4. Equivalent Variation (EV, maximum amount of income consumer would be willing to pay to avoid the price change)

1. Given ()and original income , price (,)changes from (1,1) to (2,1). Calculate CV and EV. Remember
2. CV, EV, CS at quasilinear utility function

Chapter15 Market Demand

1. Inverse demand function
2. Elasticity and Revenue, MR,
3. Income Elasticity - Show that weighted average of income elasticity is one.

Chapter16 Equilibrium

1. Demand, Supply and Equilibrium
2. Quantity Tax and Value Tax (Ad Valorem Tax)

Quantity Tax levied on Producer

Value Tax levied on Producer

Quantity Tax levied on consumer

Value Tax levied on consumer

1. Tax incidence, deadweight loss and Laffer curve(Modeling for the test of hypotheis, "Laffer effect")

where

For tax cut to increase labor supply, must hold. If elasticity of labor supply is 0.2, how large the tax rate should be to have the 'Laffer effect'?

1. Food and Energy subsidy in Iraq
2. Pareto Efficiency

Chapter18 Properties of Technology

1. Monotonicity, Convexity, production technique
2. MP(marginal Product), Diminishing MR,
3. TRS (Technical Rate of Substitution, MRTS), Diminishing TRS
4. Long run and Short run
5. Return to scale - what happens to return with scaling all inputs up by some constant

Chapter19 Profit Maximization

1. Given a firm which produces outputs with output prices and uses inputs with input prices , profit function is expressed as

For n=1, m=2,

1. Fixed and Variable Factors
2. Short run profit maximization:
3. VMP & input price
4. isoprofit line
5. comparative statics : changes and input output change
6. Long run profit maximization:
7. factor demand curve
8. inverse of factor demand curve
9. Why is the only reasonable long run level of profits for a competitive firm with CRTS to be zero?
10. Revealed Profitability
11. Revealed choice of input and output of profit maximizing firm represents:
12. it is feasible
13. it is more profitable than other choices

WAPM (weak axiom of profit maximization)

=>

=> Implication of supply curve, factor demand curve

=> Construction of possible technology

1. Profit maximization in two phase
2. minimize cost for production of any desired level of y
3. which level of output is indeed a profit maximizing level of output

Chapter20 Cost Minimization

1. Revealed Cost Min. and factor demand curve
2. AC and Unit cost curve shapes with different technologies

1. Long run and short run costs
2. s.t.
3. short run factor demand
4. short run cost function
5. s.t.
6. long run factor demand
7. long run cost function
8. Fixed cost vs. Quasi-fixed cost (only when y >0) page 373

** Conditional factor demand or cost minimizing demand (Shepherd's Lemma)

vs. profit maximizing factor demand (Hotelling's Lemma)

vs. [3]

Chapter21, 22 Cost Curves & Firm Supply

AC, AVC, AFC, MC in the short run and long run

Shutdown condition

Long run constant average cost and long run supply curve

Q. what does 2nd order condition for profit maximization imply?

Chapter23 Industry Supply

Chapter24 Monopoly

Chapter31 Exchange

Fig 31.1

Assuming a third party 'auctioneer'!

- Even if there are only two agents, it is assumed that they will behave as in a competitive market. Or assuming twp types of average demand.

Fig 31.3

Algebra of Equilibrium

Let excess demand function for good by agent be

Aggregate excess demand for good , $z^i$ is

At equilibrium,

for

Walras's law - the value of aggregate excess demand is identically zero. That is,

If one market is equilibrium at equilibrium price , we can see that the other market should be at equilibrium. In general, for markets,

we only need to find a set of prices where of the markets are in equilibrium.

=> there are only independent equations in a -good equilibrium model. That is, there really are only independent prices.

If is a set of equil. prices, then also are equil. prices as well. We can see that by letting.

Example: Refer to Chapter 6, Number 7.

Existence of a competitive equilibrium -What use would it be to build up elaboratetheories of the workings of a competitive equilibrium if such an equilibriumcommonly did not exist?

First, # of equations = # of unknowns

But, there need a crucial assumption that the aggregate excessdemand function is a continuous function.

1. Convex preferences
2. As long asall consumers are small relative to the size of the market, the aggregatedemand function will be continuous.

First Theorem of Welfare Economics - all market equilibria are Pareto efficient. A competitive market willexhaust all of the gains from trade

For Monopoly,

- No third party auctioneer.

- A knows B's demand curve and quote price for B.

Monopoly in the Edgeworth Box can be shown to be not Pareto Efficient

Fig. 31.7

The fact that the original allocation is efficient automatically determinesthe equilibrium prices.

Second Theorem of WelfareEconomics: if all agents have convex preferences, then there will alwaysbe a set of prices such that each Pareto efficient allocation is a marketequilibrium for an appropriate assignment of endowments.(The other way around of the first theorem)

First Theorem of Welfare Economics

- No consumption externality

- Each agents behave competitively (2 agents behave competitively?)

- This is only of interest if a competitiveequilibrium actually exists.

The only things that aconsumer needs to know to make his consumption decisions are the pricesof the goods he is considering consuming. Consumers don’t need to knowanything about how the goods are produced, or who owns what goods, orwhere the goods come from in a competitive market.

Second Theorem of WelfareEconomics

the problems of distribution and efficiency can be separated. WhateverPareto efficient allocation you want can be supported by the marketmechanism. The market mechanism is distributionally neutral; whateveryour criteria for a good or a just distribution of welfare, you can use competitivemarkets to achieve it.

According to the First Welfare Theorem, trade from any initialendowments will result in a Pareto efficient allocation.

According to the Second Welfare Theorem, this kind of lump-sum taxationwould be nondistortionary. Essentially any Pareto efficient allocationcould be achieved by such lump-sum redistribution.

People’s concern about the distribution of welfare can lead them to advocatevarious forms of manipulation of prices. Simple redistribution of income via lump-sum taxation

Chapter32 Production

two-consumer two-good assumption -> one consumer, one firm, and two goods.

Compare this with Figure 32.1

Robinson Crusoe - consuming leisure or gathering coconuts

1. As a firm. Robinson Crusoe maximizes profit - decidingw much labor to hire and how many coconuts to produce
2. As a consumer, Robinson Crusoe maximizes utility

A Firm or

Fig 32.2

A consumer Utility Maximization given budget constraint

Fig. 32.3

Fig. 32.4

Production and the First Theorem of Welfare Economics - if all firms act as competitive profit maximizers, then a competitive equilibrium will be Pareto efficient. (no production externality)

Production and the Second Theorem of Welfare Economics - with constant or decreasing returns to scale, any Pareto efficient allocation can be achieved through the use of competitive markets.

one consumer, one firm, and two goods.

-> to be generalized to an economy with several inputs and outputs

Coconut, Fish (CRTS) with Labor input

Robinson Crusoe & Friday

Robinson Crusoe has 10 hours (10 pound of Fish and 20 pounds of coconuts per hour)

Friday has 10 hours (20 pound of Fish and 10 pounds of coconuts per hour)

For Robinson Crusoe,

,

, , =>

For Friday,

,

, , =>

With a combined efforts, Why following?

MRS = - p1/p2 = MRT (Why?)

As consumer, the optimal consumption bundle for each consumer mustsatisfy the condition that the marginal rate of substitution between the twogoods must be equal to the common price ratio. That is MRS = - p1/p2

As a firm, or the Castaway Inc., profit maximization would give rise to MRT=- p1/p2 !

Under certain conditions, the individuals’ pursuit of privategoals will result in an allocation that is Pareto efficient overall. (1st Theorem of Welfare Economics)Furthermore,any Pareto efficient allocation can be supported as an outcome ofa competitive market, if initial endowments—including the ownership offirms—can be suitably redistributed. (2nd Theorem of Welfare Economics)

According to price signal, each agent (firm, consumers) decide their own resource allocation.

Check Appendix!!

Chapter33 Welfare

Giving everything to one person willtypically be Pareto efficient

How to revise this?

Social Welfare function adding together different consumer utilities:What is 'adding together'?

1. Majority Vote

(x,y) vs. z -> (x,z) -> z

(y,z) vs. x -> (y,x) -> x

(z,x) vs. y -> (z,y) -> y

Overall winner depends crucially on the orderin which the alternatives are presented to the voters.

1. Rank-order Vote -Rank-order voting can be manipulated byintroducing new alternatives that change the final ranks of the relevantalternatives.
2. Are there ways to “add up” preferences that don’thave the undesirable properties described above? -> Arrow's Impossibility Theorem
3. Social Welfare Function without social preferencesbetween two alternatives - following social welfare functions represent different ethical judgement.

Fair Allocation, Envy and Equity

-> A competitive equilibrium from equal division must be afair allocation.

1. Each agent has the same bundle of goods.
2. But there could be differences in taste, trade takes place and that it moves to a Pareto efficient allocation. is this Pareto efficient allocation still fair in any sense?
3. (A,B) has the same taste, not C. A and C gets trade not B. Arbitrary trading. -> B envies A and A is luckier.
4. 'Equitable' in the sense that no agent prefers any other agent’s bundle of goods to his or her own.If some agent i does prefer some other agent j's bundle of goods, we say that i envies j. Finally, if an allocation is both equitable and Pareto efficient, we will say that it is a fair allocation.

If equitable, no envies.

Fig. 33.3

Start from the same bundle of goods

Through the special mechanism of the competitive market,each agent is choosing the best bundle of goods he or she can afford at the equilibrium prices (p1, p2), Pareto efficient!

Is this equitable? Yes, then no envies.

If equitable,then it is a fair allocation since it is Pareto efficient.

Suppose it is not equitable! Then,

Say A prefers B's bundle to his own

But this also means that B's bundle cost more than A can afford.

But at the same time, B cannot afford , either since they started from an equal division such that