Lecture6 - LECTURE 6: Consumer Equilibrium (continued)...

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LECTURE 6: Consumer Equilibrium (continued) Y Recall from last class… The necessary condition is sufficient only when the ICs are convex to the origin We can verify H the ICs are convex to the origin. We can verify that if indifference curves are concave, then the point of tangency (point A) is actually the worst possible choice or the utility minimizing bundle on the consumer’s budget line X BL IC 1 IC 2 on the consumer s budget line. WHY? Point A is the minimum TU the consumer can achieve with their budgetary constraints (it lies on the lowest IC that the consumer can reach along their BL). B. Special Cases that Violate these Conditions Both of the cases shown on the next slide violate the sufficient condition of TU maximization since the ICs are not strictly convex to the origin. In both of the cases that follow, the rational consumer will move along their budget line in the direction of the arrow to point A where they achieve the highest possible IC for direction of the arrow to point A…where they achieve the highest possible IC for their BL. TU is maximized at point A, yet there is no point of tangency (corner solutions).
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Consumer Equilibrium (continued) B. Special Cases that Violate these Conditions (continued) Y IC 1 IC 1 Y X BL X BL A A MRS XY is rising In this case, the MRS is increasing (IC is concave). The reason that we get a MRS XY is constant In this case, the MRS is constant (IC is a straight line). The reason that we get a corner solution is that on the highest IC we can reach there is only one point of contact (at point A). If there were two points of contact then the TU maximizing corner solution is that on the highest IC we can reach there is only one point of contact (at point A). If the slope of the IC were equal to the slope of the BL then the solution would not be unique and we would have another set of problems (left for future micro courses). TU maximizing solution would not be unique since any combination along the BL would satisfy the necessary condition.
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Consumer Equilibrium (continued) B. Special Cases that Violate these Conditions (continued) Consider a situation where the indifference curves are strictly convex but they are much steeper than the given budget line. The necessary condition for equilibrium is not fulfilled in the budgetary range under consideration (i.e. there is no tangency at positive values of both X and Y). IC 2 Y IC 1 We know that this will lead to a “corner solution” at point A, where the highest- order indifference curve is reached. Let’s refer to this graph as “Graph #1” for now X BL A B (we will refer back to this graph soon). BUT what does this mean in economic terms? First let’s consider the economic interpretation of the slope of the indifference curve in terms of how the consumer values goods X and Y.
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Consumer Equilibrium (continued) B. Special Cases that Violate these Conditions (continued) Y + Y - + - X IC 1 X IC 1 Steeper Indifference Curve Flatter Indifference Curve For 1 extra unit of X, we give up a
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Lecture6 - LECTURE 6: Consumer Equilibrium (continued)...

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