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Economics 301
Intermediate Macroeconomics

Labor Demand

Winter 2000

Last updated: January 11, 2000

Note: These notes are preliminary and incomplete and they are not guaranteed to be free of errors. Please let me know if you find typos or other errors. 

Determining Labor Demand

Assumptions

• Workers are all alike
• Markets are competitive
• Firms act to maximize profits

Example - Starbucks coffee company

Assumptions

• Fixed capital stock and level of productivity (e.g., K = 1 espresso machine; A = 1 = index of productivity); amount of labor is allowed to vary.
• Fixed daily nominal wage for workers: W = $100/day.
• Only one good produced (Latte) and a fixed price: P = $2/cup.

A worker's real wage, in terms of lattes, is

w = W/P = ($100/day)/($2/latte) = 50 lattes/day

Production Function

A graphical representation of the production function is given below.

Determining Starbucks' demand for labor

From microeconomics we know that Starbucks will continue to hire workers until the marginal product of hiring an additional worker is equal to the marginal cost of an additional worker. The marginal product of hiring an additional worker is the extra output generated by the worker:

Marginal product of labor
= MPN = DY/DN

and the marginal cost of the worker is what the company pays for an additional work in terms of output produced:

Marginal cost of labor
= real wage = w

Hence, Starbucks stops hiring workers at the point where

MPN = w

In the example above, MPN = w = 50 when N = 3 workers. If the real wage increases to 75 lattes/day then labor demand falls to N = 2 and if w decreases to 25 lattes/day then N increases to 4. Clearly, there is an inverse relationship between Starbucks demand for labor and the real wage.

The Labor Demand Curve

The labor demand curve for a firm is a downward sloping function of the real wage. As the real wage increases workers become more expensive to firms and they demand less labor

The shape of the labor demand curve, ND, is identical to the MPN curve which is derived as the slope of the production function. Therefore, any factor that shifts the production function will also shift the ND curve

Factors that Shift the ND curve

• An increase in productivity, A, shifts up the production and so shifts the ND curve up and right
• An increase in the capital stock, K, shifts up the production and so shifts the ND curve up and right

These effects are illustrated in the figures below:

As productivity increases, the production function shifts up and simultaneously the labor demand curve shifts out and right. At a given real wage, more workers are hired and output increases.

As the capital stock increases, the production function shifts up and simultaneously the labor demand curve shifts out and right. At a given real wage, more workers are hired and output increases.

Aggregate Labor Demand

The aggregate labor demand curve - the labor demand curve for the entire economy - is simply the sum of all of the firms' individual labor demand curves.