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CORNELL UNIVERSITY FINAL EXAM Wednesday, December 16, 2009 INTERMEDIATE MICROECONOMIC THEORY ECON 3130 Professor Majumdar Fall 2009 You have 150 minutes to complete this exam. There are 135 points. Permitted Materials: Non-graphing calculators only. WARNING The exam is divided into two parts, Part A and Part B. You must answer failure to do so will result in a 10-point penalty. On the cover of each exam booklet, please state whether it includes Make sure your name is on all exam booklets used. When time is called, please put your answers to Part A in the box marked ±Part A², and put your answers to Part B in the box marked ±Part B². No exam booklets will be accepted after we leave the room. PLEASE DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO DO SO Page 1 of 6 ECON 3130
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Question 1 Answer "yes" or "no" with a brief justi±cation of your position ( a ) [ 5 points ] Let B ( p x ;p y ;m ) = f ( x;y ) : p x x + p y y ± m g be the budget set of the consumer. As usual, p x > 0 ; p y > 0 ; m > 0 : Let ( x ;y ) be the utility maximizing choice of the consumer when he is choosing in the budget set. Hence, if ( x 1 ;y 1 ) is NOT in the budget set (i.e., p x x 1 + p y y 1 > m ), it must be that u ( x 1 ;y 1 ) > u ( x ;y ) : ( b ) [ 5 points ] A consumer prefers more of the commodities x and y to less. When we hold the prices p x > 0 and p y > 0 constant, and consider variations of her income m , both x and y may be Gi/en goods. ( c ) [ 5 points ] Consumer 1 has a utility function u ( x;y ) (assume that more is preferred to less, indi/erence curves are all convex and u is twice continuously di/erentiable). She chooses a commodity bundle ( x ;y ) (all positive) on the budge set determined by p x ;p y and m (all positive). Another agent, Consumer 2, has a utility function v ( x;y ) = 2 u ( x;y ) + 3 . If Consumer 2 has the same budget set determined by the same p x ;p y and m (all positive), Consumer 2 will choose (2 x + 3 ; 2 y + 3) : ( d ) [ 5 points ] The fundamental di/erence that forces of competition make is simply this: if a competitive, pro±t-maximizing ±rm is producing and selling an output Q > 0 , it must be minimizing the cost of production of
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