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ANSWERS TO REVIEW PROBLEM 1 Economics 102 Professor Blair 1. Consider a simple economy in which the only productive resources are four workers: Ann (A), Bill (B), Carol (C), and Dave (D). Since they have different degrees of productivity, each of these workers in one day can produce various quantities of either of two goods: xylophones (X) and yogurt (Y); these quantities are presented in the table below. Thus, for example, Bill can produce in one day EITHER 2 xylophones or 3 units of yogurt. X Y A 5 1 B 2 3 C 4 3 D 1 4 The total amounts of each good produced depend on which workers are assigned to which production task. The leftmost two columns of the table below give all of the 16 possible assignments of workers to the two goods. Complete the table by computing the total output of each good corresponding to each of the allocations of workers, following the example given in the table. (You need not write "5 + 2 =", etc.) Assigned to X Assigned to Y Output of X Output of Y ABCD none 12 0 ABC D 11 4 ABD C 8 3 ACD B 10 3

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BCD A 7 1 AB CD 5 + 2 = 7 3 + 4 = 7 AC BD 9 7 BD AC 3 4 CD AB 5 4 AD BC 6 6 BC AD 6 5 A BCD 5 10 B ACD 2 8 C ABD 4 8 D ABC 1 7 none ABCD 0 11 a. Plot each of the 16 ordered pairs of outputs on the diagram on the following page. Label each point with the set of workers assigned to the production of good X, as shown for the example in the table.
b. An assignment or a llocation of resources to productive tasks is productively efficient if it is not possible to increase the output of one good without decreasing the output of the other good. (That is, no other assignment corresponds to a point in the diagram that lies to the north, east, or northeast of any efficient point.) Which allocations are productively efficient in your diagram? (You should have five such points.)

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none, A, AC, ABC, ABCD c. Connect with a straight line the efficient point on the X-axis to the nearest efficient point. Connect this point, in turn, with the next nearest efficient point. Continue to add line segments until you reach the Y-axis. These points are also efficient; they correspond to allocations in which one of the workers divides his or her day between the two tasks. (Convince yourself that this is true by computing the aggregate outputs of X and Y when A, B, and C produce X all day and worker D spends half the day producing each good. Plot this point on the graph; label it H.) The function you have graphed is the production possibility curve for this economy. d. If the economy moves from point AC to point ABC, it must sacrifice _____ 3 _____units of Y to obtain an additional _____ 2 ______ units of X. What is the opportunity cost of one unit of X in this region of the diagram? 3/2
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