10. In Example 6.4, wheat is produced according to the production function :3 = 100(KU'SLU'2) a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. 13. Does this production function exhibit increasing, decreasing, or constant returns to scale? EXAMPLE 6.4 A PRODUCTION FUNCTION FOR WHEAT Crops can be produced using dif- ferent methods. Food grown on large farms in the United States is usually produced with a capi- tal-intensive technology, which involves substantial investments in capital, such as buildings and equipment, and relatively little input of labor. However, food can also be produced using very little capital (a hoe) and a lot of labor (several people with the patience and stamina to work the soil). One way to describe the agricultural production process is to show one iso- quant (or more) that describes the combination of inputs which generates a given level of output (or several output levels). The description that follows comes from a production function for wheat that was estimated statistically.10 Figure 6.9 shows one iso- quant, associated with the pro- duction function, corresponding to an output of 13,800 bushels of wheat per year. The manager of the farm can use this isoquant to decide whether it is profitable to hire more labor or use more machinery. Assume the farm is currently operating at A, with a labor input L of 500 hours and a capital input K of 100 machine hours. The manager decides to experiment by using only 90 hours of machine time. To produce the same crop per year, he finds that he needs to replace this machine time by adding 260 hours of labor. The results of this experiment tell the manager about the shape of the wheat production iso- quant. When he compares points A (where 10'Ihe food production function on which this example is based is given by the equation q = 100(K-3L3), where q is the rate of output in bushels of wheat per year, K is the quantity of machines in use per year, and L is the number of hours of labor per year