Problem Set 10: Competitive Factor Markets - A Firm That Is

Problem Set 10 Competitive Factor Markets1 A Firm That Is Perfec

PROBLEM SET #10 --- Competitive Factor Markets 1. A firm that is perfectly competitive in product and factor markets has the following production function: L Q a. Calculate and graph the Marginal Revenue Product (MRP) for each unit of labor when the price of the firm's output is $5. Why does the MRP curve have a negative slope? b. How many units of labor will the firm hire if the wage for each worker is $35 and the product price is $5? Why? c. If the wage falls to $25 per worker, how many workers will the firm now hire? Why? Show these results in your graph in part a. Suppose that the price of the firm's product increases to $6 due to an increase in market demand for the firm's product. d. How many workers will the firm now hire if the wage for each worker is $30? Why? Show this result in a separate graph.

Paper For Above instruction

In competitive factor markets, firms aim to maximize profits by adjusting their input levels based on the marginal productivity of resources and market prices. When analyzing labor employment decisions, it is essential to understand how the marginal revenue product (MRP) of labor guides these decisions. The MRP essentially measures the additional revenue generated by hiring one more unit of labor, and it is calculated as the product of the marginal product of labor (MP) and the price of the output (P).

Given the production function, assuming it is of the form Q = aL, where Q is the output and L is the labor input, the marginal product of labor (MP) is the derivative of Q with respect to L. For simplicity, consider the production function to be linear, such that MP remains constant or varies in a predictable manner. The Marginal Revenue Product (MRP) then equals MP multiplied by the market price of the output.

In this case, with an output price (P) of $5 and an example production function, we can compute the MRP for each unit of labor. If the marginal product diminishes with each additional unit (as is common due to the law of diminishing returns), the MRP curve will decline, which explains why the MRP curve has a negative slope. This diminishing marginal productivity reflects that each additional worker contributes less to total output than the previous one, leading to a downward-sloping MRP curve.

When the wage is set at $35 per worker and the output price remains at $5, the firm will hire labor up to the point where the MRP equals the wage. If the MRP per unit of labor drops below $35, hiring additional workers would reduce profits, and thus, the firm hires only until MRP = Wage. Under these conditions, the firm equates the MRP to the wage, resulting in a specific level of employment, which can be found where the MRP curve intersects the wage line on the graph.

If the wage decreases to $25 per worker, the firm can afford to hire more labor since the cost of each worker is lower. The new equilibrium employment level increases because the MRP now exceeds the wage for additional units of labor, prompting the firm to increase its workforce up to the point where MRP equals $25. Graphing this scenario shows the shift in labor demand due to wage reduction, resulting in higher employment levels.

Furthermore, if the market price of the firm's product increases from $5 to $6, the MRP at each level of labor increases proportionally, as MRP is directly related to the output price. Consequently, the firm will find it profitable to hire more workers because the additional revenue generated by each worker now exceeds the wage cost at higher employment levels. If the wage remains at $30, the new equilibrium labor quantity will increase, as the higher MRP justifies more employment. Graphical representation of this change shows a shift of the MRP curve upward, leading to higher employment levels where MRP intersects the wage line.

In conclusion, the firm's optimal employment decisions hinge on the relationship between the MRP curve and the wage rate. Changes in output prices and wages significantly impact the quantity of labor employed, illustrating the fundamental principles of competitive labor markets and marginal productivity theory.

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