Suppose that the organization you are working for wants to increase its annual production, measured in units, by 50%. Also, assume that your organization's output i. is an increasing function of only capital and labor, and ii. that the law of diminishing returns to a single factor holds for both capital and labor.

a. Which of the assumptions above implies that the marginal product of labor is greater than zero for any level of employment? Explain.

b. Given that the marginal product of labor is greater than zero for any level of employment, does it follow that the average product of labor is an increasing function of employment? Explain.

c. Given that the marginal product of labor decreases with employment, does it follow that the average product of labor will become, at one point, negative? Explain.

d. Given our assumptions, and holding capital constant, in order to increase output by 50% should your organization increase its annual employment by more, less or by exactly 50%? Explain why.

e. Suppose now that, in addition to changing its employment, your organization can increase its capital as well. Without using any math, explain why the information about diminishing returns to each single factor is consistent with any type of returns to scale.

f. Given your knowledge about your organization, do you think that in order to increase output by 50%, your organization should increase its scale of production by exactly 50%, less than 50% or by more than 50%? Explain your reasoning, and associate it to your assessment of your organization's returns to scale.

g. Suppose that your organization's production function is represented by a Cobb-Douglas production function. Provide a specific production function that is consistent with the question's assumptions and with your assessment of its returns to scale as in part f.