Lecture1 - ECON 301 LECTURE #1 REVIEW: Consumer Equilibrium...

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1 ECON 301 – LECTURE #1 REVIEW: Consumer Equilibrium (Utility Maximization) The consumer desires to maximize their Total Utility subject to their budget constraint. Let’s consider the case where the consumer has the choice between 2 goods, X and Y. Max U(X,Y) subject to P X X + P Y Y = M X,Y Using ECON 201 logic, we know that for the consumer to reach an equilibrium he/she must have no further incentives to shift consumption among the two goods (in terms of Utility). This implies that the last unit purchased of X and the last unit purchased of Y must give the consumer the same “satisfaction”. Suppose, for example, that P X = 2 and P Y = 1. We should notice the relationship between P X and P Y is simply P X = 2P Y . Our ECON 201 logic is that if X costs twice as much as Y … to be worth paying double for X, its marginal utility (utility per additional unit) must be twice the marginal utility of Y in equilibrium. This implies that; MU X = 2MU Y Rearranging, MU X = MU Y 2 1 or simply, MU X = MU Y P X P Y Of course, this condition extends to the case of multiple (more than two) goods as follows: MU 1 = MU 2 = … = MU n P 1 P 2 P n !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Now that we have taken ECON 211, we can arrive at this conclusion quantitatively. Using the Lagrangian technique learned in ECON 211, we can set up the consumer’s problem in general as: L : Max U(X,Y) + ! (M – P X X – P Y Y) X,Y
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2 Taking the First Order Conditions, we get: " L / " X = FOC X U # X ! P X = 0 (1) " L / " Y = FOC Y U # Y ! P Y = 0 (2) Where, U # X = Marginal Utility of good X. U # Y = Marginal Utility of good Y. Rearrange (1) and (2) to isolate ! on the LHS… ! = U # X / P X from (1) (3) ! = U # Y / P Y from (2) (4) Equate (3) and (4) to get, U " X = U " Y P X P Y or simply, MU X = MU Y P X P Y which is the consumer’s equilibrium condition that we arrived at above using our ECON 201 logic and intuition. This condition is central to microeconomics and this course. We will often use variations of the equilibrium condition above, for example, MU X = P X MU Y P Y which says that the ratio of the marginal utilities of two goods is proportional to the ratio of the prices of the two goods. Also, this says that the MRS XY is equal to the relative prices of X and Y (the price ratio). !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Some popular utility functions used in economics are of the forms: U(x,y) = aX $ Y % Cobb-Douglas Preferences U(x,y) = aX + bY Perfect Substitutes Utility U(x,y) = min{aX , bY) Liontief Preferences – Perfect Compliments
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3 U(x,y) = X + aY 1/2 Quasi-linear Preferences Quasi-linear preferences are useful in economic applications because they allow us to ignore wealth effects. This enables us to approach the problem using partial equilibrium rather than general equilibrium techniques. These have a similar shape to Cobb-Douglas preferences. Expectations for Diagrams, Graphs and Charts in this Course
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Lecture1 - ECON 301 LECTURE #1 REVIEW: Consumer Equilibrium...

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