Exercise 1: An economy has two individuals (A and B ) and produce: two good: (X and Y') using one input (labor, [). Each individual is endowed with 100 units of labor. There are two competitive firms, one produces good X and the other one produces good Y. Technology for producing the goods is given by the following production functions: X = 10 Y = In)1: where 8 = 5 1+ (-1)'+-412(6-AM/B + 1+ (-1)1+4]2(7-AM/8 and A is the last digit of your Student ID#. Both individuals have the same prefererences. These can be represented by the following utility function:: LA(CA, YA) = 31n(@A) +61(94) a. Determine how much of each good is produced for the following two cases: 1. Half of all available labor is used to produce X and half to produce Y. 2. 7/8 of all available labor is used to produce X and 1/8 to produce Y b. Find the Production Possibilities Frontier and graph it. Obtain the Mariginal Rate of Transformation analytically (as a function of X"). c. For each of the case: (a.1) and(a.2), assume that total output of the two goods produced is split evenly among the two individuals. In each case, determine if the resulting allocation (@A, @2, MA, 32 ) is efficient. Also, if possible, compare the two allocations to determine which one is more socially desirable (whether one of them makes both people better off than the other). Explain