Unformatted text preview: ontief utility function: U(x,y) = min{2X , 3Y} meaning, U(x,y) = {2X {3Y if 2X < 3Y if 3Y < 2X so we need to find some combinations of goods X and Y that result in U(x,y) = 1. Consider the following 3 points: X 1/2 1/2 1 Y 1/3 1 1/3 2X 2(1/2) = 1 2(1/2) = 1 2(1) = 2 3Y 3(1/3) = 1 3(1) = 3 3(1/3) = 1 U(x,y) = min{2X , 3Y} min {1 , 1} = 1 min {1 , 3} = 1 min {2 , 1} = 1 25 Each of these points yields exactly one unit of utility as defined by our Liontief unit indifference curve. The rigid preference structure for a Liontief consumer gives us the Lshaped indifference curve with a kink at the corner point. The corner point is where both 2X and 3Y give us one unit of utility (in general, where X = Y). This occurs in our example when X = 1/2 (or generally, when X = 1/) and Y = 1/3 (or generally, when Y = 1/). The straight line (or kink line) joining the point of origin and the corner points for this family of indifference curves has a slope determined by 2X = 3Y or Y = 2/3X (or generally, /).
Y 1 A Slope = 2/3 = / 1/3 Kink B Indifference curve X 1/2 1 The kink point is the only real point of interest to us when dealing with Liontief preferences (or production). If we compare the kink point (1/2 , 1/3) with point A (1/2 , 1) on the vertical segment and point B (1 , 1/3) on the horizontal segment, it should be clear that while these three points lead to the same utility level for the consumer, point A requires more of good Y and point B requires more of good X than the kink point does to achieve the same utility level. This means that the kink point gives this consumer the "best" (most efficient in terms of resources) combination of goods X and Y according to a fixed proportion (i.e. X = Y). Thus, this type of function has a rather rigid structure in the sense that extra amounts of the goods beyond these proportions are completely ruled out because they do not add any extra utility to the consumer (and with strictly positive prices, these superfluous goods have a cost to the consumer). As a result of the argument above, the indifference curve for these preferences has an Lshape with the vertical segment representing all of...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
 Spring '10
 sning
 Economics

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