Question

1. Prunella raises peaches. Where L is the number of units of labor she uses and T is the number of units of land she uses, her output is f(L, T) = L 1 2 T 1 2 bushels of peaches. (a) On a graph, plot some input combinations that give her an output of 4 bushels. Sketch a production isoquant that runs through these points. (b) Does this production function exhibit constant, increasing or decreasing returns to scale? Why? (c) In the short run, Prunella can not vary the amount of land she uses. On a graph, draw a curve showing Prunellas output as a function of labor input if she has 1 unit of land. Locate the points on your graph at which the amount of labor is 0, 1, 4, 9, and 16 and label them. The slope of this curve is known as the marginal product of labor. Is this curve getting steeper or flatter as the amount of labor increase? (d) In the long run, Prunella can change her input of land as well as of labor. Suppose that she increases the size of her orchard to 4 units of land. On the graph you plotted in part (c), draw a new curve showing output as a function of labor input. Also draw a curve showing marginal product of labor as a function of labor input when the amount of land is fixed at 4.

Answer 1

Answer satisfys output (a) input Combinations that equals to 4 bushels. fCLT) = 1² The 4 = 12 TV 2 T= 16 87.(2,8) 4+ ABO_1827 16,19 2 + 2 4 6 8 10 12 14 16 L (6) f(L,T) = 1/2 f(ah, aT) = (AL) 2 (0)2 & 1220 ( positive) f(aLaT) = 2/27/2 2 1/2 - 1/2 f(ALAT) = à f(LT) Constant returns to scale. (() slope of the Curve is marginal Product of labor and this cune. getting glatter as the amount of labour increases.

land, used from (d) Assuming she has 1 unit of and she is previously unt of labor, extra output 1 more labor = 12-1 & 0.41 4 more labor = 15-2 0.24 calcules. f(LT) - L af - I S ƏL QI ар) S 4,13&sg y = 0.25.

Output Red MPL line Red line Blue line 4 8 12 16 Labour
answer of part E