midtermsolutions+_Spring2004

midtermsolutions+_Spring2004 - Econ 51: Midterm Answer Key...

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Answers are in bullets, following the questions. 1 True/False questions (36 points) (a) Let x and y be the consumption in two states of the world. The utility function u ( x, y )=10+2 x 2 +6 y 2 +21 y 3 +7 x 3 does not represent vNM preferences. False. We can rewrite u ( x, y )= 1 4 v ( x )+ 3 4 v ( y )w ith v ( x )=10+8 x 2 +28 x 3 ,wh ichis of the vNM form. (b) An individual with vNM utility v ( x )= e 7 x is risk averse. False. v 00 ( x )=49 e 7 x is positive, so the individual is not risk averse. (c) There are apples ( a ) and bananas ( b ). Tom and Rob have identical utility function u ( a, b )=max( a, 15). There are 20 apples and 20 bananas on the island. Any point in the Edgeworth box is Pareto e cient. False. For example, giving 17 apples and 10 bananas to Rob is not Pareto e cient: by taking one apple from Tom and giving it to Rob, Rob is better o f while Tom is not worse o f (his utility remains 15). (d) There are apples ( a ) and bananas ( b ). Tom and Rob have identical utility function u ( a, b )=log( a ). A f rm can transform one apple to 3 bananas. In equilibrium it must be that p a =3 p b . False. Nobody in this market wants bananas, so in equilibrium the f rm will not produce and the equilibrium price for bananas will be zero. (e) There are apples ( a ), bananas ( b ), and cucumbers ( c ). Y = { ( a, b, c ): a 0 ,b =2 a, c = 3 b } is a f rm’s production set. This f rm can transform apples into both bananas and cu- cumbers. False. Both apples and bananas are inputs. The f rm transforms apples and bananas into cucumbers. (f) Country A can produce 2 apples or 5 bananas with one unit of labor. Country B can produce 3 apples or 6 bananas with one unit of labor. This means that country B has
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This note was uploaded on 03/19/2011 for the course ECON 51 taught by Professor Tendall,m during the Winter '07 term at Stanford.

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midtermsolutions+_Spring2004 - Econ 51: Midterm Answer Key...

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