Class 5s - Department of Economics LeBow College of...

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Department of Economics Fall 2009 LeBow College of Business Microeconomics 301 Drexel University Professor Stehr Class 5 Outline 1. Derivation of demand functions 2. Income and substitution effects of price change 3. Social Security Payments and the CPI Derivation of demand functions Key Equations: 1) Tangency condition Assuming no corner solution, the utility maximizing bundle occurs where the indifference curve is tangent to the budget line which means MRS = Px / Py. Recall that the MRS = MU x / MU y . The marginal utility of X is the additional utility derived from a little more consumption of good X. Mathematically, it can be expressed as the partial derivative of the utility function with respect to X. MU x = δ U / δ X 2) Budget constraint The utility maximizing bundle lies on the budget constraint: We can use these equations to derive the demand curve for the consumer. Extended Example: Suppose a consumer has utility function U = XY where X = the quantity of good X consumed and Y = the quantity of good Y consumed and income = I. a) Find expressions for MU x and MU y . 1
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marginal utility of Y is in fact equal to X. (Hint: Suppose X 1 and Y 1 represent quantities of X and Y. The marginal utility of X is the increase in total utility that arises from consuming one more unit of X, so the MUx may be obtained by subtracting U(X 1 ,Y 1 ) from U(X 1 +1,Y 1 ). c) Derive the demand curve for X. (Hint: Begin with the expression implying that the MRS must equal the price ratio and solve for Y. Substitute this expression for Y into the equation for the budget constraint and solve the resulting equation for X. You should obtain an expression for X as a function of prices and income. 2
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Class 5s - Department of Economics LeBow College of...

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