The labor demand curve of a purely competitive seller:
What exactly is your question?
Is it something like: what is the slope (elasticity) of the demand for labor labor faced by a producer who sells in a perfectly competitive market?
I would argue that selling in a perfect competitive market has nothing do do with the shape of the demand for labor. If the firm hires a significant portion of the local labors, or if the type of labor hired has special skills, the demand curve for labor will be relatively inelastic. If the firm is a small employer hiring common laborers, the curve will be flat (elastic).
The demand curve for labor in a purely competitive market represents the relationship between the quantity of labor demanded by firms and the wage rate. The shape of the demand curve depends on various factors, including the characteristics of the labor market and the firm's ability to substitute labor with other factors of production.
To determine the slope or elasticity of the labor demand curve, you can follow these steps:
1. Identify the factors affecting labor demand: Consider the characteristics of the labor market, such as the availability of skilled or unskilled labor and the level of competition among firms.
2. Determine the relationship between the wage rate and the quantity of labor demanded: The demand for labor is generally negatively related to the wage rate. Higher wage rates tend to decrease the quantity of labor demanded, while lower wage rates increase the quantity of labor demanded.
3. Calculate the elasticity of labor demand: Elasticity measures the responsiveness of quantity demanded to changes in price (wage rate). The formula to calculate elasticity is:
Elasticity of labor demand = (% change in quantity of labor demanded) / (% change in wage rate)
To determine the elasticity, you need to calculate the percentage change in the quantity of labor demanded and the percentage change in the wage rate.
4. Interpret the elasticity value: The elasticity value determines the responsiveness of labor demand to changes in the wage rate. If the value is greater than one, the demand for labor is elastic, meaning that a small change in the wage rate leads to a proportionally larger change in the quantity of labor demanded. If the value is less than one, the demand is inelastic, indicating that a change in the wage rate has a smaller effect on the quantity of labor demanded.
Remember that the shape of the labor demand curve can vary depending on the specific characteristics of the labor market and the firm's position within it. It may not necessarily be determined solely by whether the market is purely competitive or not.