Lecture6-1

# Lecture6-1 - ECON 301 LECTURE #6 ENDOWMENTS AND INCOMES...

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1 ECON 301 – LECTURE #6 ENDOWMENTS AND INCOMES Let’s look at how we define the budget line in general equilibrium theory. Recall that given prices, P X and P Y , and income, M, the budget constraint of the consumer is written as: P X X + P Y Y = M We can rewrite this equation as Y = M – P X X P Y = _M_ - _P X _ · X P Y P Y so that the budget line is a straight line with… slope = - _P X _ ! 0 and vertical intercept = _M _ P Y P Y As the price of good X goes up (everything else remaining the same), the budget line rotates around its vertical intercept while the consumer income remains the same. Y X Y = M / P Y – (P X / P Y )X BL 1 BL 2 M / P Y

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2 In general equilibrium theory, the consumer income, M, is no longer exogenously fixed. Instead, we go one step further and define the consumer income, M, in terms of the concept of a consumer’s endowment income as follows: M e = P X · ! X + P Y · ! Y where " X and " Y denote the amounts of goods X and Y originally owned by the consumer, respectively. That is, [1] P X · " X is the market value of endowments in good X evaluated at price P X . [2] P Y · " Y is the market value of endowments in good Y evaluated at price P Y . As a result, instead of being fixed, the consumer endowment income M e fluctuates with market prices. So now we will have a new budget line. Using the consumer endowment income, M e , instead of the fixed consumer income, M, we can write the equation of the budget constraint as follows: P X X + P Y Y = M e P X X + P Y Y = P X · ! X + P Y · ! Y and we can rewrite this equation as: Y = P X · " X + P Y · " Y - P X X P Y = _ P X · " X + P Y · " Y _ - _P X _ · X P Y P Y = _P X _ · " X + " Y - P X · X P Y P Y so that the new budget line is a straight line with… slope = - _P X _ ! 0 and vertical intercept = __P X _ · " X + " Y P Y P Y When the consumer’s income is defined in terms of endowments, as the price of good X goes up, ceteris paribus, the budget line rotates around the endowment point ( " X , " Y ) instead of the vertical intercept.
3 So let me explain the difference between the concept of exogenous income, M, and the endowment income, M e . Before, we were studying the theory of consumer equilibrium in a self-contained framework where the consumer’s income was exogenously fixed (exogenous = determined from outside the modeling process). In that case, we were concerned only with the optimizing behavior of a single consumer without any relationship to other consumers or producers in the economy. Now, in general equilibrium theory, we are studying the optimizing behavior of a consumer in the context of the inter relationship with other consumers and producers. We go one step further to endogenize the consumer income (endogenous = determined within the modeling process). That is, the endowment income now depends on both the market prices (P X and P Y ) and the original endowment points ( " X , " Y ). When prices change, the endowment income also changes and hence, the

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## Lecture6-1 - ECON 301 LECTURE #6 ENDOWMENTS AND INCOMES...

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