Problem Set #5: Production and Cost
1. Consider the following production function for your company
a. suppose the labor input is increased by 13 percent next year (with K held constant), determine the approximate percentage change in output
b. What type of returns to scale characterizes this production function? How do you know?
c. Based on the production function, determine an expression for the marginal product of labour.
d. What is the marginal product of the 5th worker if 3 units of capital are employed in your company?
2. You recently replace Antoine, the manager of Division 3, despite Antoine’s strong external sales record. Division 3 produces frozen drinks. Frozen drinks are relatively simple to make. Ignoring the ingredients, it requires only labour and a blender. As you begin reviewing the company’s production information, you learn that labour is paid $8 per hour and the last worker produced 100 drinks per hour. The company rents blenders for $15 per hour and the marginal product of capital is 120 drinks per hour. What do you think Antoine could have done to keep his job? Explain
3. How would each of the following affect the firm's marginal, average, and average variable cost curves?
a. An increase in wages
b. A decrease in material costs
c. The government imposes a fixed amount of tax.
d. The rent that the firm pays on the building that it leases decreases
4. A politician campaigning for upcoming elections visits a plant to win workers’ votes and is surprised that the idea of promoting legislation to increase safety in the workplace is not supported by workers. Present reasons for the workers reaction
5. The management of Neha Industries is considering a plan to terminate a new employee. The action stemmed from documented evidence supplied by the firm's accounting department that this new employee did not add as much to the firm's overall output as did a worker hired two weeks earlier. Based on this evidence, do you agree that the latest worker hired should be fired? Explain
6. You were recently employed by Roop Industries to evaluate their hiring practices as it relates to the profit maximization goal of the firm. You observed that salespersons in the company are paid “w” wages per day to sell product x. More salespersons increase sales but at a decreasing rate (positive downward sloping portion of the MP curve). Selling more units of x does not affect the price of the product (P). You also observed that for salespersons presently employed, w=MPL*P (wages=value marginal product) but MPL > APL (producing where MPL curve lies above APL curve). Advice Roop based on your observation, particularly, is the firm making a profit from hiring salespersons?