2-6-09 - Draw something downward sloping and tangent to the...

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Microeconomics – Class Notes – 2/6/09 Workbook (study guide): Problems : 10, 11, 13, 14, 18 Combining indifference curves and budget constraints Lagrangian method IGNORE THIS METHOD As individuals, we want to maximize the utility function: U(X1, X2) Slope of budget constraint = opportunity cost Slope of indifference curve = marginal rate of substitution
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Interior solution – when you are consuming both goods at the same time 1. Corner solution (perfect substitutes, quasilinear) – spending all of your money on one good and none of your money on the other good. 2. Indifferent curve not smooth (perfect complements)
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NOTE: Cobb-Douglas – never have a corner solution – always spending money on a combination of the two goods. APPROACH (to maximization of utility problems): 1 st thing you do – write down the budget constraint because it is assumed that the consumer spends all of his/her income 2 nd thing you do - When I’m maximizing my utility, the slope of the indifference curve = slope of budget constraint
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When he asks you to draw the utility curve, it DOES NOT HAVE TO BE EXACT:
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Unformatted text preview: Draw something downward sloping and tangent to the budget constraint. The equation that you reach after setting the slope of the budget constraint equal to the indifference curve this equation is what you use to determine the point at which the budget constraint and indifference curves are tangent to each other. o The line F = 2E intersects the budget constraint at (50, 100), which is the tangent point. o Draw your indifference curve tangent at that point. Problem #1 Make sure that you designate either Football and Basketball as either X or Y and keep your axes consistent (for when you plot them on the graph). The exponents in cobb-douglas utility function (only!) tell you that your percentage of income spent on each good When your exponents do NOT add to up to 1 you need a monotonic transformation to a cobb-douglas utility function that DOES have exponents that DO add up to 1: Use this procedure to check your answer after finding the utility function:...
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2-6-09 - Draw something downward sloping and tangent to the...

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