Chapter 5: The Production Process and Costs Flashcards
Production Function
Defines the maximum amount of output that can be produced with a given set of inputs.
Most production processes involve machines of some sort (referred to by economists as capital) and people (labor)
Production Inputs
A production process utilizes at least two inputs, capital and labor, to produce output.
K: the quantity of capital
L :the quantity of labor
Q: the level of output produced
The production function determines the maximum amount of output that can be produced with K units of capital and L units of labor.
Short-Run versus Long-Run Decisions
A manager must determine how much of each input to use to produce output.
In the short run, some factors of production are fixed, and this limits your choices in making input decisions.
Fixed Factors of Production
The inputs a manager cannot adjust in the short run.
Capital is generally fixed in the short run.
Variable Factors of Production
The inputs a manager can adjust to alter production in the short run
(labour, energy, and raw materials variable even in the short run).
Short Run Decision: Example
Suppose capital and labor are the only two inputs in production and that the level of capital is fixed in the short run.
In this case, the only short-run input decision to be made by a manager is how much labor to utilize.
The short-run production function is essentially only a function of labor since capital is fixed rather than variable. If K* is the fixed level of capital, the short-run production function may be written as
Fixed Capital
If Capital is fixed in the short run, then more labor is needed to produce more output because increasing capital is not possible.
Long Run Decisions
the manager can adjust all factors of production.
If it takes a company three years to acquire additional capital machines, the long run for its management is three years, and the short run is less than three years.
Measures of Productivity
Measures the productivity of inputs used in the production process.
The three most important measures of productivity are total product, average product, and marginal product.
Total Product (TP)
The maximum level of output that can be produced with a given amount of inputs.
Example: the total product of the production process described in Table 5-1 when 5 units of labor are employed is 1,100. Since the production function defines the maxi- mum amount of output that can be produced with a given level of inputs, this is the amount that would be produced if the 5 units of labor put forth maximal effort.
Average Product (AP)
A measure of the output produced per unit of input.
Marginal Product (MP)
The marginal product (MP) of an input is the change in total output attributable to the last unit of an input.
Negative Marginal Product
A negative marginal product means that the last unit of the input actually reduced the total product.
If a manager continued to expand the number of workers on an assembly line, he or she would eventually reach a point where workers were packed like sardines along the line, getting in one another’s way and resulting in less output than before.
Increasing Marginal Returns
Range of input usage over which marginal product increases.
Decreasing (Diminishing) Marginal Returns
Range of input usage over which marginal product declines.
Negative Marginal Returns
Range of input usage over which marginal product is negative.
Phases of Marginal Returns
As the usage of an input increases, the marginal product initially increases (increasing marginal returns), then begins to decline (decreasing marginal returns), and eventually becomes negative (negative marginal returns).
Level of Inputs
The second role of the manager is to ensure that the firm operates at the right point on the production function. (When to operate)
Value Marginal Product
The value of the output produced by the last unit of an input.
Profit-Maximizing Input Usage
To maximize profits, use inputs at levels at which the marginal benefit equals the marginal cost.
An input should be until its cost equals VMP. For labor, w = VMP defines a firm’s profit maximizing use of labor.
This is an instance of derived demand: the demand for an input depends on productivity (derived demand: land, offices, labor).
When the cost of each additional unit of labor is w, the manager should continue to employ labor until VMPL = w in the range of diminishing marginal product.
VMPL = w0 in the range of diminishing marginal returns
Note: The downward-sloping portion of the VMPL curve defines demand for labor by a profit-maximizing firm; it shows the relationship between the wage rate and the amount of labor a firm will want to hire at that rate.
Law of Diminishing Marginal Returns
The marginal product of an additional unit of an input will at some point be lower than the marginal product of the previous unit.
Linear Production Function
A production function that assumes a perfect linear relationship between all inputs and total output.
Where a and b are constants. With a linear production function, inputs are perfect substitutes. There is a perfect linear relationship between all the inputs and total output
Linear Production Function: Example
Suppose it takes workers at a plant four hours to produce what a machine can make in one hour. In this case, the production function is linear with a = 4 and b = 1:
This is the mathematical way of stating that capital is always 4 times as productive as labor. Furthermore, since F(5,2) = 4(5) + 1(2) = 22, we know that 5 units of capital and 2 units of labor will produce 22 units of output.
Marginal Product for a Linear Production Function
If the production function is linear and given by Q = F(K, L) = aK + bL
then:
MPK = a
MPL = b
For a linear production function, the marginal product of an input is simply the co- efficient of the input in the production function. This implies that the marginal product of an input is independent of the quantity of the input used whenever the production func- tion is linear; linear production functions do not obey the law of diminishing marginal product.
Cost Function
Determines the profit-maximizing level of output.
Total Cost
Sum of fixed and variable costs.
Short-Run Costs
The short run is defined as the period over which the amounts of some inputs are fixed. In the short run, the manager is free to alter the use of variable inputs but is “stuck” with existing levels of fixed inputs.
Because inputs are costly whether fixed or variable, the total cost of producing output in the short run consists of (1) the cost of fixed inputs and (2) the cost of variable inputs.
Short-run total cost are called fixed costs and variable costs.
Fixed Costs (FC)
Costs that do not change with changes in output; include the costs of fixed inputs used in production.
All sunk costs are fixed, but not all fixed costs are sunk.
Variable Costs (VC(Q))
Costs that change with changes in output; include the costs of inputs that vary with output.
Short-Run Cost Function
A function that defines the minimum possible cost of producing each output level when variable factors are cost-minimizing.
Since all costs fall into one category or the other, the sum of fixed and variable costs is the firm’s short-run cost function.
A Common Misconception about Costs
Large firms have lower costs than smaller firms because they produce larger quantities of output
Average Fixed Cost (AFC)
Fixed costs divided by the number of units of output.
Since fixed costs do not vary with output, as more and more output is produced, the fixed costs are allocated over a greater quantity of output. As a consequence, average fixed costs decline continuously as output is expanded.
Average variable cost (AVC)
Provides a measure of variable costs on a per-unit basis.
Variable costs divided by the number of units of output.
Average Total Cost (ATC)
Average total cost is analogous to average variable cost, except that it provides a measure of total costs on a per-unit basis.
Total cost divided by the number of units of output.
Marginal Cost (MC)
The change in total costs arising from a change in the managerial control variable Q.
The cost of producing an additional unit of output, that is, the change in cost attributable to the last unit of output.
When only one input is variable, the marginal cost is the price of that input divided by its marginal product. Marginal product increases initially, reaches a maximum, and then decreases. Because marginal cost is the reciprocal of marginal product times the input’s price, it decreases as marginal product increases and increases when marginal product is decreasing.
Relations Among Costs
The shapes of the curves ( average total, average variable, average fixed, and marginal costs) indicate the relation between the marginal and average costs presented in those tables.
The marginal cost curve intersects the ATC and AVC curves at their minimum points. This implies that when marginal cost is below an average cost curve, average cost is declining, and when marginal cost is above average cost, average cost is rising.
ATC AND AVC Curves
TC and AVC curves get closer together as output increases, because the only difference in ATC and AVC is AFC.
The difference between average total costs and average variable costs is ATC − AVC = AFC. Because average fixed costs decline as output is expanded, as in Figure 5-12, this difference between average total and average variable costs diminishes as fixed costs are spread over increasing levels of output.
Sunk Costs
A cost that is forever lost after it has been paid. In other words, sunk costs are the amount of these fixed costs that cannot be recouped.
A decision-maker should ignore sunk costs to maximize profits or minimize losses.
Long-Run Costs
In the long run, all costs are variable because the manager is free to adjust the levels of all inputs.
Long-Run Average Cost Curve
A curve that defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production.
Economies of Scale
Exist whenever long-run average costs decline as output increases.
When there are economies of scale, increasing the size of the operation decreases the minimum av- erage cost.
Diseconomies of Scale
Exist whenever long-run average costs increase as output increases.
After a point, further increases in output lead to an increase in average costs.
Constant Returns to Scale
Exist when long-run average costs remain constant as output is increased.
Sometimes the technology in an industry allows a firm to produce different levels of output at the same minimum average cost.
Economic of Scope
Exist when the total cost of producing two products within the same firm is lower than when the products are produced by separate firms.
Economies of scope exist when the total cost of producing Q1 and Q2 together is less than the total cost of producing Q1 and Q2 separately, that is, when C(Q1, 0) + C(0, Q2) > C(Q1, Q2)
Cost Complementarity
When the marginal cost of producing one type of output decreases when the output of another good is increased.
The multi- product cost function C(Q1, Q2) = f + aQ1Q2 + (Q1)2 + (Q2)2
1. Exhibits cost complementarity whenever a < 0.
2. Exhibits economies of scope whenever f − aQ1Q2 > 0.
