George J. Bordas (2021). Labor Economics, 8th Ed
3. Labor demand
3.1 - The production function
The production function is represented with a two axis graph, with employee-hour E on
the horizontal axis, and the capital K on the vertical one. The shape of the curve is
concave, presenting marginally diminishing returns.
The marginal product of labor (which we denote by MPE) gives the change in output
resulting from hiring an additional worker, holding constant the quantities of all other
inputs. Similarly, the marginal product of capital (or MPK) gives the change in output
resulting from a one-unit increase in the capital stock, holding constant the quantities of
all other inputs.
We define the average product of labor (or APE) as the amount of output produced by the
average worker. This quantity is defined by APE = q/E. Moreover, we can find the profit
maximizing function π = pq - wE - rK. From the firm’s point of view, all of these prices are
constants, beyond its control. A firm that cannot influence prices is said to be a perfectly
competitive firm. Because a perfectly competitive firm cannot influence prices, it
maximizes profits by hiring the “right” amount of labor and capital.
3.2 - The short run
To obtain the dollar value of what each additional worker produces, we multiply the
marginal product of labor times the price of the output. This quantity is called the value
of the marginal product of labor and is given by VMPE = p × MPE. Because the value of
marginal product equals the marginal product of labor times the (constant) price of the
output, the value of marginal product curve is simply a “blown-up” version of the marginal
product curve. We define the value of average product of labor as VAPE = p × A PE
We can now derive the short-run demand curve for labor. This demand curve tells us what
happens to the firm’s employment as the wage changes, holding capital constant. It takes
into account the industry’s expansion on output prices.
The requirement that firms hire workers up to the point where the value of marginal prod-
uct of labor equals the wage gives the firm’s “stopping rule” in its hiring decision—that is
also known as the marginal productivity condition. w = VMPE
3.3 - The long run
An isoquant gives the combinations of labor and capital that produce the same level of
output. The absolute value of the slope is called the marginal rate of technical
substitution, ΔK / ΔE = − MPE / MPK.
3. Labor demand
3.1 - The production function
The production function is represented with a two axis graph, with employee-hour E on
the horizontal axis, and the capital K on the vertical one. The shape of the curve is
concave, presenting marginally diminishing returns.
The marginal product of labor (which we denote by MPE) gives the change in output
resulting from hiring an additional worker, holding constant the quantities of all other
inputs. Similarly, the marginal product of capital (or MPK) gives the change in output
resulting from a one-unit increase in the capital stock, holding constant the quantities of
all other inputs.
We define the average product of labor (or APE) as the amount of output produced by the
average worker. This quantity is defined by APE = q/E. Moreover, we can find the profit
maximizing function π = pq - wE - rK. From the firm’s point of view, all of these prices are
constants, beyond its control. A firm that cannot influence prices is said to be a perfectly
competitive firm. Because a perfectly competitive firm cannot influence prices, it
maximizes profits by hiring the “right” amount of labor and capital.
3.2 - The short run
To obtain the dollar value of what each additional worker produces, we multiply the
marginal product of labor times the price of the output. This quantity is called the value
of the marginal product of labor and is given by VMPE = p × MPE. Because the value of
marginal product equals the marginal product of labor times the (constant) price of the
output, the value of marginal product curve is simply a “blown-up” version of the marginal
product curve. We define the value of average product of labor as VAPE = p × A PE
We can now derive the short-run demand curve for labor. This demand curve tells us what
happens to the firm’s employment as the wage changes, holding capital constant. It takes
into account the industry’s expansion on output prices.
The requirement that firms hire workers up to the point where the value of marginal prod-
uct of labor equals the wage gives the firm’s “stopping rule” in its hiring decision—that is
also known as the marginal productivity condition. w = VMPE
3.3 - The long run
An isoquant gives the combinations of labor and capital that produce the same level of
output. The absolute value of the slope is called the marginal rate of technical
substitution, ΔK / ΔE = − MPE / MPK.
