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midtermsolutions+_Spring2004

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

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Econ 51: Midterm Answer Key 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 ) with v ( x ) = 10 + 8 x 2 + 28 x 3 , which is 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 ff while Tom is not worse o ff (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 fi 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 fi 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 fi rm’s production set. This fi rm can transform apples into both bananas and cu- cumbers. False. Both apples and bananas are inputs. The fi 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 a comparative advantage in the production of both apples and bananas.
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