finding optimum

finding optimum - Lily Wong (CUTIE) Econ 1011 6d. The...

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Lily Wong (CUTIE) Econ 1011 6d. The Calculus of Optimization As we know from the previous section, the goal of consumer is to Maximize Utility. There are two conditions to Maximize Utility: 1. Slope of Indifference Curve = Slope of Budget Line In other words, Brief Definitions : *Marginal Rate of Substitution (MRS) MRS is the maximum amount of y that a consumer is willing to give up to get one more x. Thus, MRS = Y / X = dY/dX = Slope of IC Or MRS = MUx/MUy where MUx = U/ X = U/ X; MUy = U/ Y = U/ Y Proof : Given: U(X,Y) Take total differential dU = U/ X • dX + U/ Y • dY dU = MUx • dX + MUy • dY Along the IC, dU = 0 Thus, 0 = MUx • dX + MUy • dY dY/dX = MUx/MUy *Slope of Budget Line (also called Budget Constraint) In Figure 6.d.1, the blue line is the Budget Constraint. In order to find the intercept of X which represents the quantity of X, we have to divide the income (I) by the price of X (Px). Similarly, we have to divide the income (I) by the price of Y (Py) to find the intercept of Y which represents the quantity of Y. Thus, The intercept of X = I/ Px The intercept of Y = I/ Py Then, Slope of B.C.= Rise/Run = (I/ Py) / (I/ Px) = (I/ Py) • (Px /I)
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finding optimum - Lily Wong (CUTIE) Econ 1011 6d. The...

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