Question

Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm's expansion path.

Short answer

A decrease in labor cost will shift the expansion path to become steeper, signifying an increased employment of labor relative to capital at each level of output. This is visually represented by an upward pivoting of the expansion path over time.

Step-by-step solution

Understand the Problem Context

Firstly, one should acknowledge an economic downturn, which reduces the labor costs by half, and this situation is anticipated to persist indefinitely. When labor becomes cheaper, it becomes more efficient to employ labor than capital, which changes the firm's expansion path and production decisions.

Recreate the Initial Graph

Start with a graph that represents the initial condition, where the cost of labor and capital are equivalent, rendering an isoquant straight down the middle of the graph. The isoquant, which represents different combinations of labor and capital that produce the same level of output, should be tangential to the lowest isocost line (depicting choices of capital and labor combinations at a given cost).

Depict Economical Downturn

Since labor costs fall by fifty percent, readjust the isocost line, as it can now be obtained at half the previous cost. Rotate the isocost line counterclockwise around the capital axis. It will intercept the vertical axis further up since more labor can be hired for the same cost.

Draw the New Expansion Path

The new expansion path should be drawn to reflect the lower cost of labor. It will slope upwards and become steeper than the original path, since more labor will be used for the same level of output. It should be drawn such that it is tangential to all isoquants, representing the optimal choice of capital and labor at each level of output.

Key concepts

Economic Downturn

An economic downturn is a period where the economy slows down, leading to fewer jobs, lower consumer spending, and a general decrease in economic activity. Such downturns can have significant impacts on businesses, especially in terms of costs and pricing.
For firms, an economic downturn often results in decreased demand for products and services. This change can lead to adjustments in production practices and strategies.
During these periods, firms must find ways to stay competitive and manage costs efficiently. Thus, examining and potentially restructuring their expansion path becomes crucial. This path is the direction a firm moves when it expands production.

• It considers how resources such as labor and capital are allocated.
• The path changes as cost structures or output levels alter due to external economic conditions.

Understanding these conditions helps firms adapt their strategic planning in response to economic downturns.

Labor Costs

Labor costs refer to all expenses that a business must incur to hire workers. These include wages, benefits, and payroll taxes.
When labor costs fall, it becomes cheaper for companies to hire more workers or retain their existing workforce. This is particularly beneficial during an economic downturn, as it helps businesses maintain their operations without overextending financial resources.
Cheaper labor can encourage firms to consider hiring additional staff, investing in training, and potentially increasing productivity.

• Lower labor costs can lead to more favorable conditions for labor-intensive industries.
• It provides firms with an opportunity to adjust their production functions to rely more heavily on labor.

This reshuffling can change a firm's expansion path significantly, as companies take advantage of reduced costs to optimize resource allocation.

Isoquants

Isoquants are vital concepts in production theory. An isoquant is a curve that shows all possible combinations of two inputs, like labor and capital, that result in the same level of output.
These curves help businesses understand how different combinations of inputs affect output, aiding in decision-making about resource allocation.
In the context of an economic downturn with lowered labor costs, isoquants help analyze how shifting focus from capital to labor affects production.

• Isoquants are typically downward sloping, indicating a trade-off between labor and capital.
• The curve does not change direction, as the same output is reached despite using different input ratios.

Businesses use isoquants to find the most efficient production methods through changes in input costs and availability.

Isocost Line

An isocost line represents all combinations of inputs that cost the same amount of money. It's a helpful tool for firms trying to decide the most cost-effective way to produce goods.
The line shifts based on changes in input costs, such as labor or capital. When labor costs decrease, the isocost line rotates outward from the capital axis because more labor can be hired for the same expenditure.
The intersection of isocost lines with isoquants shows the optimal mix of inputs for a given cost.

• When labor becomes cheaper, the isocost line rotates counterclockwise, showing that more labor and less capital are being used.
• This rotation can lead to a steeper expansion path for firms optimizing their resource allocation.

The manipulation of isocost lines allows businesses to better align their input strategy with current economic conditions, such as a downturn.