Income Offer Curves and Engel Curves





We have seen that an increase in income corresponds to shifting the budget line outward in a parallel manner. We can connect together the demanded bundles that we get as we shift the budget line outward to construct the income offer curve. This curve illustrates the bundles of goods that are demanded at the different levels of income, as depicted in Figure 6.3A. The income offer curve is also known as the income expansion path. If both goods are normal goods, then the income expansion path will...
 A 14 Optimization
 A p
 A RAq
 A12 The Product Rule and the Chain Rule
 A13 Partial Derivatives
 A4 Inverse Functions
 A5 Equations and Identities
 A6 Linear Functions
 A7 Changes and Rates of Change
 Adjustments for Differences among Assets
 Analyzing Present Value for Several Periods
 Appendix  2 3 4 5 6 7 8 9 10
 Applications
 Asset Markets
 Assets with Consumption Returns
 Assumptions about Preferences
 AT1 Second derivatives
 AU MU2Ax2
 Auction Design
 Automobile Pollution
 Ax i MU2
 Behavior of the MRS
 Behavioral Economics
 Bonds
 Boundary optimum The optimal consumption involves consuming zero units of good 2 The indifference curve is not tangent to the budget line
 Budget Constraint
 Budget Line Changes
 Calculating Gains and Losses
 Castaways
 Chapter  2
 Choice of the Interest Rate
 Choosing Taxes
 Comparative Advantage
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 Comparing Ways to Allocate Apartments
 Comparison to Private Goods
 Constant Elasticity Demands
 Constructing a Model
 Constructing Utility from Demand
 Consumer Demand
 Consumer Preferences
 Consumers Surplus  2
 Cost Curves
 Cost Minimization
 Decentralized Resource Allocation
 Demand  2
 Demand for a Discrete Good
 Diminishing Marginal Product
 Diminishing Technical Rate of Substitution
 Dip Sp
 Discrete Goods  2
 Diversification
 Elasticity and Demand
 Elasticity and Revenue
 Equilibrium and Efficiency
 Equilibrium in a Market for Risky Assets
 Equilibrium in the Long
 Example Cobb Douglas Demand Functions
 Example Cobb Douglas Preferences
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 Expected Utility
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 Fixed and Variable Factors
 From Consumers Surplus to Consumers Surplus
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 H ux
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 IlWl0 ixi 1 220 U2x2
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 Information Technology  2
 Interpreting the Change in Consumers Surplus
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 Llkyr
 LockIn
 M
 Marginal Revenue Curves
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 MaxpiDpi p2 pi
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 Mean Variance Utility
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 Moral Hazard and Adverse Selection
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 MRy py
 Msxpyi 2121 cVi
 Mu2
 Network Externalities
 Oligopoly
 Optimal Choice
 Optimal choice The optimal consumption position is where the indifference curve is tangent to the budget line
 Optimization and Equilibrium
 Other Interpretations of Consumers Surplus
 Other Interpretations of the MRS
 P 0 Ay
 P Px t P22 p pxpx
 P v7 16
 Pareto Efficiency  2
 Perfect Complements
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 Pq
 Preferences
 Present Value A Closer Look
 Price Discrimination
 Private Provision of the Public Good
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 Production
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 Public Goods
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 Quasilinear Preferences
 Quasilinear preferences Each indifference curve is a vertically shifted version of a single indifference curve
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 Rights Management
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 Social Welfare Functions
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 Supply
 Systems Competition
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 Technology
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 Tt0m m ri61
 Two Goods Are Often Enough
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 Uncertainty
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 Utility Functions and Probabilities
 MvS y2
 Voting
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 Welfare
 Welfare Maximization
 Which Way Is Best
 Mp1
 Xajpup2ttia 1 a
 X2
 XICIN3ddV
 Y  2 3 4 5 6 7
 Yt y