Unformatted text preview: $216 per week in income and the price of cola is $2 per bottle. Suppose the price of cola falls to $1 per bottle. [i] Find Julian's total demand response to the price change. [ii] Find Julian's response to the price change due to the substitution effect. [iii] Finally, find Julian's response to the price change due to the income effect. [b] Is cola a normal good or an inferior good to Julian? [c] Draw the diagram to explain the Slutsky decomposition of the two effects on Julian's overall demand for cola. 88 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, PX and PY, and income, M, the budget constraint of the consumer is written as: PXX + PYY = M We can rewrite this equation as Y = M PXX PY = _M_ - _PX_ X PY PY so that the budget line is a straight line with... slope = - _PX_ 0 PY and vertical intercept = _M_ PY 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 M / PY Y = M / PY (PX / PY)X BL2 BL1 X 89 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: Me = PX X + PY Y where X and Y denote the amounts of goods X and Y originally owned by the consumer, respectively. That is,  PX X is the market value of endowments in good X evaluated at price PX.  PY Y is the market value of endowments in good Y evaluated at price PY. As a result, instead of being fixed, the consumer endowment income Me fluctuates with market prices. So now we will have a new budget line. Using the consumer endowment income, Me, instead of the fixed consumer income, M, we can write the equation of the budget constraint as follows: PXX + PYY = Me PXX + PYY = PX X + PY Y and we can rewrite this equation as: Y = PX X + PY Y - PXX PY = _ PX X + PY Y _ - _PX_ X PY PY = _PX_...
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