The firm's problem Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two inputs of production; each unit of labor is paid the market wage (w), and each unit of capital is rented at the rental price of capital (r). Output (Y) is therefore a function of labor and capital, or Y = f (K, L), and is sold at the market price (P). The goal of this firm is to maximize profit given the price of bots, the wage rate, the rental rate of capital, and production technology by choosing its labor and capital inputs. Fill in the following equations with the firm's profit maximization problem: Profit Revenue - Labor Cost - Capital Cost Labor Cost + Capital Cost - Revenue Profit-maxi Revenue - Labor Cost iring an additional unit of labor will affect profit. To do this, the firm can compare the change in revenue from hiring the cost of that extra worker. The additional output produced by an extra unit of labor is equal to the Revenue - Labor Cost - Capital Cost marginal p h bot sells for the market price (P), the change in revenue from hiring an additional worker is Revenue - Capital Cost w Fill in the following equations with the firm's profit maximization problem: Profit = Revenue - Labor Cost - Capital Cost Pf (K, L) – WL – rK Pf (K, L) – WL – rK Profit-maxi rmine how hiring an additional unit of labor will affect profit. To do this, the firm can compare the change in revenue from hiring wL+ rK – Pf (K, L) bor against the cost of that extra worker. The additional output produced by an extra unit of labor is equal to the marginal p Because each bot sells for the market price (P), the change in revenue from hiring an additional worker is Pf(K, L) – WL in cost is Pf(K, L) – rK W Firms will continue to hire workers until the change in profit is Given this condition, which of the following equations correctly Profit-maximizing firms must determine how hiring an additional unit of labor will affect profit. To do this, the firm can compare the change in revenue from hiring an additional unit of labor against the cost of that extra worker. The additional output produced by an extra unit of labor is equal to the marginal product of labor (MPL). Because each bot sells for the market price (P), the change in revenue from hiring an additional worker is and the change in cost is W P MPL F ntinue to hire workers until the change in profit is Given this condition, which of the following equations correctly Y P profit-maximizing labor choice of the firm? PXY MPL PL = ? W W PX MPL PL = MPL MPL Р III Profit-maximizing firms must determine how hiring an additional unit of labor will affect profit. To do this, the firm can compare the change in revenue from hiring an additional unit of labor against the cost of that extra worker. The additional output produced by an extra unit of labor is equal to the marginal product of labor (MPL). Because each bot sells for the market price (P), the change in revenue from hiring an additional worker is and the change in cost is W I W Firms will continue to hire workers until the rofit is Given this condition, which of the following equations correctly describes the profit-maximizing labor choice W X Y MPL = P W MPL = W Р W X MPL W= MPL Р Given this condition, which of the following equations correctly Firms will continue to hire workers until the change in profit is describes the profit-maximizing labor choice of the firm? positive MPL: Р W negative OMPL= W Р equal to zero W = MPL P MPL = w XP Demonstrate your understanding of the previous concepts in the following example. Suppose the price of a bot is equal to $2, and the market wage rate is $12. Moreover, suppose the marginal product of labor for this firm is equal to the following: MPL = 14-L On the graph, use the blue line (circle symbol) to show the firm's demand for labor. Then, place the black point (plus symbol) on the graph to indicate the real wage and the profit-maximizing quantity of labor. Note: Dashed drop lines will automatically extend to both axes. ? 20 O 18 Labor 16 14 12 Real w, labor UNITS OF OUTPUT (Bots) PER UNIT OF LABOR 10 8 0 0 2 4 6 14 16 18 20 10 12 UNITS OF LABORPrevious question

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