16.11. Ted and Joe eachJconsume peaches, x, and plums, y: The consumers have identical utility functions, with MS}? = 10m], _MRS_'d = IWTM Together, they have 10 peaches and 10 plums. Verify whether each of the following allocations is on the contract curve: 3) Ted: 8 plums and 9 peaches; Joe: 2 plums and 1 peach. b) Ted: 1 plum and l peach; Joe: 9 plums and 9 peaches. 16.12. Two consumers, Ron and David, together own 1,000 baseball cards and 5,000 Pokemon cards. Let M denote the quantity of baseball cards owned by Ron and yR denote the quantity of Pokemon cards owned by Ron. Similarly, let xD denote the quantity of baseball cards owned by David and yD denote the quantity 01' Pokemon cards owned by David. Suppose, further, that for Ron, MESH = yn/xn, while for David, MRSDW = ynlhn. Finally, suppose xi! = 800, yR = 800, x0 = 200, and yD = 4,200. a) Draw an Edgeworth box that shows the set of feasible allocations in this simple economy. b) Show that the current allocation of cards is not economically efcient. c) Identify a trade of cards between David and Ron that makes both better off. (Note: There are many possible answers to this problem.) 16.17. Two rms together employ 10 units of labor (I) and 10 units of capital (It). The marginal rate of technical substitution of each firm is given by: MRTSllk = kill] and MRTSZlk = 4k2fl2. Which of the following input allocations satisfy the condition of input efciency? a) Firm 1 uses 5 units of labor, 5 units of capital; Firm 2 uses 5 units of labor, 5 units of capital. b) Firm 1 uses 5 unit of labor, 8 units of capital; Firm 2 uses 5 units of labor; 2 units of capital. 16.18. Two rms together employ 20 units of labor and 12 units of capital. For Firm 1, which uses 5 units of labor and 8 units of capital, the marginal products of labor and capital are MP1] = 20 and MP\": = 40. For Firm 2, which uses 15 units of labor and 4 units of capital, the marginal products are MP21= 60 and MPZII = 30. a) Draw an Edgeworth box for inputs that shows the allocation of inputs across these two firms. b) Is this allocation of inputs economically efcient? Why or why not? If it is not, identify a reallocation of inputs that would allow both rms to increase their outputs