Question

Consider a garment production factory sells its product in a perfectly competitive gar- ment market and to produce clothing, the garment factory hires tailor from a perfectly competitive labor market and faces a demand curve of LD = 50−2w and a supply curve of LS = 8w, where w is the wage rate is dollars per hour and L is employment of tailors.

Plot the demand and supply curves and indicate the equilibrium point?

Answer 1

The equilibrium point is found by setting the given labor demand equation, LD = 50−2w, equal to the labor supply equation, LS = 8w. Solving these equations gives us an equilibrium wage of $5 per hour and an equilibrium quantity of 40 tailors hired.

Step-by-step explanation:

The given question involves plotting the demand and supply curves for labor in a perfectly competitive labor market. According to the question, the garment factory is operating in a market where there is a perfectly competitive output and labor market, meaning that the factory can hire as many tailors as required at the market wage, and sell its products at market prices.

Given the demand curve for labor (LD) as 50−2w and the supply curve for labor (LS) as 8w, where w represents the wage rate, we can plot these two linear equations on a graph. The point where the two curves intersect represents the equilibrium in the labor market. At this point, the quantity of labor demanded equals the quantity of labor supplied.

To find the equilibrium wage and quantity of tailors hired, set LD equal to LS:

50 − 2w = 8w

• 50 = 10w
• w = $5 (equilibrium wage)

Substitute the value of w back into either the demand or supply equation to find the equilibrium quantity of labor (L).

• LS = 8(5)
• L = 40 tailors (equilibrium quantity)

At a wage rate of $5 per hour, the factory will hire 40 tailors in equilibrium. This is the point where the wage rate leads to the quantity of labor supplied being exactly equal to the quantity of labor demanded by employers.