Behind the Supply Curve: Inputs and Costs

A firm is an organization that produces goods or services for sale.
Production is the process of turning inputs into outputs.
A production function is the relationship between the quantity of inputs a firm uses and the quantity of output it produces.
A fixed input is an input whose quantity is fixed for a period of time and cannot be varied.
A variable input is an input whose quantity the firm can vary at any time.

The long run is the period in which all inputs can be varied.
The short run is the period in which at least one input is fixed.
The total product curve shows how the quantity of output depends on the quantity of the variable input for a given quantity of the fixed input.

The total product curve slopes upward because more wheat is produced as more workers are employed.
It becomes flatter because the marginal product of labor declines as more workers are employed.

The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input.
Marginal product of labor (MPL) is the change in output resulting from a one-unit increase in the amount of labor input. Expressed as: MPL = \frac{\Delta Q}{\Delta L}
MPL equals the slope of the total product curve.
If MPL declines as more workers are hired, the total product curve gets flatter.

Diminishing returns to an input: an increase in the quantity of that input, holding the levels of all other inputs fixed, reduces that input’s marginal product.

With more land (fixed input) each worker can produce more. This shifts the total product curve up.
The MPL of each worker is higher when the farm is larger; the MPL curve shifts up, too.

The MPL is defined as the increase in the quantity of output when you increase the quantity of that input by one unit.
A unit of labor could be an additional hour of labor, an additional week, or a person-year.
Consistency in the unit of measure is key.

A fixed cost is a cost that does not depend on the quantity of output produced. It is the cost of the fixed input.
A variable cost is a cost that depends on the quantity of output produced. It is the cost of the variable input.
example, the dining room of a deli is a fixed input.

The total cost of producing a given quantity of output is the sum of the fixed cost and the variable cost of producing that quantity of output. Expressed as: TC = FC + VC
The total cost curve shows how total cost depends on the quantity of output.
The total cost curve becomes steeper as more output is produced, a result of diminishing returns.
With diminishing returns, additional units of output require more and more labor; therefore the cost increases.

The marginal cost is the change in total cost generated by one additional unit of output. Expressed as: MC = \frac{\Delta TC}{\Delta Q}
where \Delta = change, TC = total cost, and Q = quantity of output.
The marginal cost curve is upward sloping because there are diminishing returns to inputs.
As output increases, the marginal product of the variable input declines.
More of the variable input must be used to produce each additional unit of output as the amount of output already produced rises.
Since each unit of the variable input must be paid for, the cost per additional unit of output also rises.

Average total cost (often referred to simply as average cost) = total cost per unit of output produced. Expressed as: ATC = \frac{TC}{Q}
Average fixed cost = fixed cost per unit of output produced. Expressed as: AFC = \frac{FC}{Q}
Average variable cost = variable cost per unit of output produced. Expressed as: AVC = \frac{VC}{Q}

Increasing output has two opposing effects on average total cost:
- The spreading effect: The larger the output, the more output over which fixed cost is spread, leading to lower average fixed cost.
- The diminishing returns effect: The larger the output, the more variable input required to produce additional units, which leads to higher average variable cost.

Marginal cost slopes upward because of diminishing returns.
Average variable cost also slopes upward but is flatter than the marginal cost curve.
Average fixed cost slopes downward because of the spreading effect.
The marginal cost curve intersects the average total cost curve from below, crossing it at its lowest point.

At high levels of output, the spreading effect is weaker than the diminishing returns effect.

The minimum-cost output is the quantity of output at which average total cost is lowest—the bottom of the U-shaped average total cost curve.
Three general principles are always true about a firm’s marginal cost and average total cost curves:
1. At the minimum-cost output, average total cost is equal to marginal cost.
2. At output less than the minimum-cost output, marginal cost is less than average total cost and average total cost is falling.
3. At output greater than the minimum-cost output, marginal cost is greater than average total cost and average total cost is rising.

Marginal cost curves often slope downward as the output goes from zero up to some low level, and they slope upward at higher levels of production.
The initial downward slope occurs when employing more workers allows them to specialize in various tasks.
This specialization leads to increasing returns to the hiring of additional workers and results in the marginal cost curve sloping downward.
Once enough workers exhaust the benefits of specialization, diminishing returns to labor set in and the marginal cost curve slopes upward.
Typical marginal cost curves have the “swoosh” shape.

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