Chapter 14: Problem 3

Derive the firm's demand curve for labour, when there are many variable factors. Briefly discuss the substitution effect, output effect and the profit maximizing effect.

Short Answer

Expert verified

Answer: The steps to derive a firm's demand curve for labor are: 1. Understand the profit-maximizing condition for labor (W = MRPL) 2. Examine the substitution effect (negative relationship between labor demand and wage rate) 3. Examine the output effect (change in input factor prices affecting production cost and output) 4. Combine the substitution effect and the output effect (both leading to a decrease in labor demand when wages increase) 5. Plot the demand curve for labor (showing a downward-sloping relationship between wage rate and quantity of labor demanded)

Step by step solution

Understand the profit-maximizing condition for labor

To maximize profit, the firm must find the optimal mix of inputs (labor and other variable factors). The profit-maximizing condition for labor is when the wages paid to workers (W) is equal to the marginal revenue product of labor (MRPL), which is the additional revenue generated by employing one more unit of labor. Mathematically, this condition is represented as : W = MRPL Where, W: Wage rate MRPL: Marginal Revenue Product of Labor

Examine the substitution effect

The substitution effect occurs when a firm replaces one input factor with another, in response to a change in the relative prices of the input factors. When the price of labor increases compared to other variable factors, the firm may substitute labor with these other inputs to minimize its cost. This negative relationship between labor demand and its wage rate is the substitution effect.

Examine the output effect

The output effect occurs when a change in input factor prices affects the overall production cost, which in turn influences the firm's level of output. If the labor cost increases, the overall production cost will also rise, which may lead the firm to produce less. This, in turn, reduces the demand for labor. The output effect reinforces the negative relationship between labor demand and its wage rate.

Combine the substitution effect and the output effect

The firm's overall demand for labor is determined by the combined effect of the substitution effect and the output effect. As the wage rate increases, both the substitution effect and the output effect lead to a decrease in the demand for labor.

Plot the demand curve for labor

To derive the firm's demand curve for labor, plot the quantity of labor (L) on the horizontal axis and the wage rate (W) on the vertical axis. The demand curve will show the downward-sloping relationship between the wage rate and the quantity of labor demanded, as a result of the substitution effect, output effect, and the profit-maximizing condition. The firm's demand curve for labor will slope downwards from left to right, demonstrating the inverse relationship between the wage rate and the quantity of labor demanded.