***PLEASE NOTE – An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers***

Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?^0.5?^0.5 bushels of apples.

a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis.

b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve?

c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?

d. In the long run, the farmer can change both his amount of land and his amount of labor. Suppose he increases the size of his orchard to 16 units of land. Add to the graph you drew in (b) a new curve showing output as a function of labor when land is fixed at 16.