A. From the table below, answer the questions that follow.
Demand and Supply of Labor Data
Employment Total Output Product Price Wage Rate
50 708 $1.27 $6
51 760 1.26 7
52 810 1.25 8
53 858 1.24 9
a. Calculate the marginal revenue product (MRP) at each level of employment.
b. How many units of labor will this firm hire in order to maximize its profits?
B. Consider the following payoff matrix in which the numbers indicate the profits in millions of dollars for a duopoly based either on a high-price or a low-price strategy.
High Price Low Price
Firm B High Price A = $500, B = $500 A = $650, B = $250
Low Price A = $250, B = $650 A = $300, B = $300
a. What will be the result (in profits) when each firm chooses a high-price strategy?
b. What will be the result when Firm A chooses a low-price strategy while Firm B maintains a high-price strategy?
c. What will be the result when each firm chooses a low-price strategy?
d. Determine the Nash equilibrium for this matrix.
A. See the attached file.
a. MRPL = (change in TR)/(change in labor)
b. The firm will hire more workers as long as MRPL>MCL. That's true when L=51 but not when L=52, so the firm will hire 51 ...
This solution shows how to calculate the Marginal Revenue Product of Labor (MRPL) and use it to determine how many workers a firm should hire to maximize profit.
*Bonus* How to find the Nash equilibrium in a payoff matrix involving two oligopolistic firms.