Prunella raises peaches. Where L is the number of units of labor she uses and T is

Question:

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 the graph below, plot some input combinations that give her an output of 4 bushels. Sketch a production is oquant that runs through these points. The points on the is oquant that gives her an output of 4 bushels all satisfy the equation.
(b) This production function exhibits (constant, increasing, decreasing) returns to scale.
(c) In the short run, Prunella cannot vary the amount of land she uses. On the graph below, use blue ink to draw a curve showing Prunella€™s 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 ________ of ________. Is this curve getting steeper or flatter as the amount of labor increase? ________.

(d) Assuming she has 1 unit of land, how much extra output does she get from adding an extra unit of labor when she previously used 1 unit of labor? ________units of labor? ________. If you know calculus, compute the marginal product of labor at the input combination (1, 1) and compare it with the result from the unit increase in labor output found above. ________.
(e) 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. Use red ink to draw a new curve on the graph above showing output as a function of labor input. Also use red ink to draw a curve showing marginal product of labor as a function of labor input when the amount of land is fixed at 4.