The document describes a production function for the food industry where output is determined by capital and labor. It asks how labor productivity, as measured by average product of labor, changes if a firm reduces output during a recession by laying off workers. It also asks whether a Japanese firm would do better than a comparable American firm during a recession, given that Japanese firms typically lay off a smaller proportion of workers.

1. Suppose production in the food industry is given by Q = K 0 . 4 L 0 . 6 where K represents units
of capital and L represents units of labor. The government is concerned about labor productivity,
as measured by the average product of labor, and is worried about how it will change if the
economy sees a recession.
(a) (4 points) Use calculus to calculate how the average product of labor changes as labor
increases. (You can treat capital as constant). Use your calculation to answer how labor
productivity, as measured by the average product of labor, changes during a recession if the
manager of a firm has to reduce output and decides to lay off workers (increase, decrease, or
stays the same)?
(b) (4 points) Assume that the production function for these firms is given by the description
above. During recessions, American firms lay off a larger proportion of their workers than
Japanese firms do. Using this information, would you expect a Japanese firm to do better or
worse than a comparable American firm in light of a recession, all else held constant? Use your
answer from part (a) to explain.
Solution
y = k 0.4
0.1* k 0.4
= 0.05 *
k; k = 3.17
y = k 0.4
= 1.59
c = y