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Lecture5 - Lecture 5 Calculating marginal utility Utility...

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Lecture 5 Calculating marginal utility Utility functions and indifference curves Examples of MRS, MU Intro to demand curves
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Quick Note on Partial Derivatives Suppose U(X,Y) = KX, where K is a constant. 𝜕𝑈 𝜕𝑋 = ?? 𝜕𝑈 𝜕𝑋 = 𝐾 Let U(X) = AXY = AYX = (AY)X 𝜕𝑈 𝜕𝑋 = derivative of U holding everything but X constant, i.e., “as if” AY were constant. Or: let (AY) be equivalent to K in the first example. 𝜕𝑈 𝜕𝑋 = (AY) Let U(X,Y) = AXY = (AX)Y 𝜕𝑈 𝜕𝑌 = ??? 𝜕𝑈 𝜕𝑌 = AX
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Marginal Utility We will be concerned with two classes of utility function: U(X, Y) = XY (or 10XY, .5XY, etc.: AXY, A is constant) U(X, Y) = X + Y (or 5X + 2Y, etc: aX + bY, a and b constant Marginal utility = partial derivatives: U(X,Y) = AXY: 𝜕𝑈 𝜕𝑋 = 𝐴𝐴 ; 𝜕𝑈 𝜕𝑌 = 𝐴𝐴 U(X,Y)=aX+bY; 𝜕𝑈 𝜕𝑋 = 𝑎 ; 𝜕𝑈 𝜕𝑌 = b
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Utility functions and indifference curves An indifference curve is a set of points where utility is constant.
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