UGBA 101A Week Five & Six: Production Flashcards
The production decisions of firms can be understood in three steps
Production Technology
Cost Constraints
Input Choices
Production Technology
How inputs (such as labor, capital, and raw materials) can be transformed into outputs
Cost Constraints
How inputs (such as labor, capital, and raw materials) can be transformed into outputs
A cost constraint is a limitation or restriction on the amount of resources, such as money, time, or materials, that can be spent on a specific project, activity, or decision.
Input choices
Just as a consumer is constrained by a limited budget, the firm is concerned about the cost of production and the prices of labor, capital, and other inputs
Theory of the Firm
Explanation of how a firm makes cost-minimizing production decisions and how its cost varies with its output
Why do Firms Exist?
Firms offer a means of coordination that is extremely important and would be sorely missing if workers operated independently.
Firms eliminate the need for every worker to negotiate every task that he or she will perform and bargain over the fees that will be paid for those tasks.
How do firms avoid individual bargaining?
They have managers that direct the production of salaried workers – they tell workers what to do and when to do it, and the workers (as well as the managers themselves) are simply paid a weekly or monthly salary
What 3 categories can factors of production be divided into?
Labor
Material
Capital
What does a Production Function show?
- production function: showing the highest output that a firm can produce for every specified combination of inputs.
q = F (K,L)
output Y, input X
What do production functions describe?
Production functions describe what is technically feasible when the firm operates efficiently – that is, when the firm uses each combination of inputs as effectively as possible
Short Run vs Long Run for the Production Function
- Short run Period of time in which quantities of one or more production
factors cannot be changed. - Fixed input Production factor that cannot be varied.
- Long run - Amount of time needed to make all production inputs variable
Average product
output per unit of a particular input
Marginal product
additional output produced as an input is increased by one unit
average product of labor =
output/labor input = q/L
marginal product of labor =
change in output / change in labor input (change q / change l)
slopes of the product curve
what does the total output curve show?
how do you obtain the average product curve?
how do you obtain the marginal product curve?
The total output curve in (a) shows the output produced for different amounts of labor input.
the average product curve is obtained from output (q) divided by labor (slope of the line from the origin to point A)
the marginal product curve is obtained from plotting the tangent to the total product curve at each point (change in q / change in L)
can the average and marginal product curves intersect?
yes
When the marginal product is above the average product, is the average product increasing or decreasing?
when the marginal product curve is above the
average product, the average product is increasing.
When the marginal product is below the average product, is the average product increasing or decreasing?
decreasing
ex. When the labor input is greater than 5 units, the
marginal product is below the average product, so the
average product is falling.
Once the labor input exceeds 9 units, the marginal product becomes negative, so that total output falls as more labor is added.
When total output is maximized, what is the marginal product?
when total product is optimized, it reaches vertex (turning point), so the slope of the tangent at this point is 0. this means the marginal product is also 0!
What is the marginal product beyond the maximum total product point?
negative
In general, how do we determine the average product of labor at any one point?
In general, the average product of labor is given by the slope of the line drawn from the origin to the corresponding point on the total product curve.
In general, how do we determine the marginal product of labor at any one point?
In general, the marginal product of labor at a point is given by the slope of the total product at that point.
(can be related to the tangent to the total product at any point)
The Law of Diminishing Marginal Returns
The principle that as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease
How to calculate labor productivity?
Output per unit of labor
Average product of labor for an entire
industry or for the economy.
How can labor productivity increase?
Labor productivity (output per unit of labor) can increase if there are improvements in technology, even though any given production process exhibits diminishing returns to labor
Consumers in the aggregate can increase their rate of consumption in the long run only by increasing the _________ they produce
total amount
Stock of capital
total amount of capital available for use in production
technological change
development of new technologies allowing factors or production to be used more effectively
What do isoquants curve show?
Isoquants Curve show all possible combinations of inputs that yield the same output.
The term “isoquant,” broken down in Latin, means “equal quantity,” with “iso” meaning equal and “quant” meaning quantity. Essentially, the curve represents a consistent amount of output. The isoquant is known, alternatively, as an equal product curve or a production indifference curve.
What do isoquant maps show?
Isoquant maps are graphs combining a number of isoquants, used to describe a production function
What describes the firm’s production function?
(production with two variable inputs)
a set of isoquants, or isoquant map describes the firm’s production function
these are banana shaped curves with each variable input on x and y axis, showing the varying combinations of x and y that can produce the same output
By drawing a horizontal line at a particular level of capital for an isoquant map, what do we observe?
diminishing marginal returns
in figure 5.5, we can observe that each additional unit of labor generates less and less additional output
How do isoquants show input flexibility?
Isoquants show the flexibility that firms have when making production decisions:
They can usually obtain a particular output by substituting one input for another.
It is important for managers to understand the nature of this flexibility.
How does diminishing marginal returns apply to production with two variable inputs?
Even though both labor and capital are variable in the long run, it is useful for a
firm that is choosing the optimal mix of inputs to ask what happens to output as
each input is increased, with the other input held fixed.
Because adding one factor while holding the other factor constant eventually leads to lower and lower incremental output, the isoquant must become steeper as more capital is added in place of labor and flatter when labor is added in place of capital.
There are also diminishing marginal returns to capital. With labor fixed, the
marginal product of capital decreases as capital is increased
What is the marginal rate of technical substitution (MRS)?
MRS - Amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant.
MRTS = - Change in capital input / change in labor input
= -∆K / ∆L (for a fixed level of q)
Diminishing MRS
Additional output from increased use of labor= (MP�)(∆L)
Reduction in output from decreased use of capital=(MP�)(∆K)
(MPL ) ( L K Δ ) + (MPx )(Δ ) = 0
The additional output from increased use of labor + reduction in output from decreased use of capital should equal 0 as MRS is when output remains constant
Now, by rearranging terms we see that
(MPL ) (MPx ) = ( L K − Δ / Δ ) = MRTS
How are isoquants shaped?
downward sloping and convex (like indifference curves)
What does the slope of the isoquant at any point measure? What ability of the firm is this?
The marginal rate of technical substitution (MRS), which is the ability of the firm to replace capital with labor (2 variables) while maintaining the same level of output
What is the special case of production function: fixed proportions production function? (or Leonitief production function)
fixed-proportions production function Production function with L-shaped
isoquants, so that only one combination of labor and capital can be used to
produce each level of output.
What situations does the fixed-proportions production function (Leonitief production function) describe?
The fixed-proportions production function describes situations in which
methods of production are limited
What is the special case of production function when the isoquants have inputs that are perfect substitutes?
When the isoquants are straight lines, the MRTS is constant. Thus, the rate at which capital and labor can be substituted for each other is the same no matter what level of inputs is being
used.
negative diagonal straight lines
Points A, B, and C represent three different capital-labor combinations that
generate the same output �3 (Figure 5.7)
Does adding one variable alone in the case of fixed proportions production function increase output?
adding one variable alone does not increase output.
this is because isoquants are L-shaped in this case, so only one combination of the variables can be used to produce a given output. therefore simply adding one more of one variable does not change the output
returns to scale
rate at which output increases as inputs are increased proportionally
increasing returns to scale
situation in which output more than doubles when all inputs are doubled
constant returns to scale
situation in which output doubles when all inputs are doubled
decreasing returns to scale
situation in which output is less than doubled when all inputs are doubled
Do returns to scale need to be uniform across all possible levels of output?
Returns to scale need not be uniform across all possible levels of output. For
example, at lower levels of output, the firm could have increasing returns to
scale, but constant and eventually decreasing returns at higher levels of output
Returns to scale very considerably across firms and industries. Other things being equal, the greater the returns to scale, the ____ the firms in an industry are likely to be
larger
When a firm’s production process exhibits constant returns to scale as shown by a movement along line 0A in part (a), the isoquants are _____ as output increases proportionally
equally spaced (6.3)
when there are increasing returns to
scale as shown in (b), the isoquants ______ as inputs are increased along
the line.
move closer together (6.3)
How does a long-run production function differ from a short-run production function?
The short-run production function refers to a period where at least one input is fixed, limiting the ability to adjust production levels. In contrast, the long-run production function represents a period where all inputs can be adjusted, allowing for greater flexibility in production choices.
Why is the marginal product of labor likely to increase initially in the short run as more of the variable input is hired?
Initially, adding more workers allows individuals to specialize.
What is the difference between a production function
and an isoquant?
An isoquant shows different combinations of inputs at a specific output level, while production functions show different outputs with maximizing combinations.
Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you about the
nature of the production function? What does each of these shapes tell you about the MRTS?
Convex: with one input fixed, the variable will face MRTS.
Linear: Outputs are perfect substitutes, MRTS is equal between outputs.
L-Shaped: Production can not be increased without both inputs being added at a fixed rate. MRTS is 0 without the combination of both outputs.
Can an isoquant ever slope upward?
No – output would change but it is fixed in an isoquant
Explain the term “marginal rate of technical substitution.” What does a
MRTS = 4 mean?
The amount at which one input (capital) can be reduced when one extra unit of another input (labor) is used so that output remains constant.
What does a MRTS = 4 mean?
You can increase one unit of an input (labor) for 4 units of a currently used input (capital).
- Joe owns a small coffee shop, and his production function is q = 3KL where q is total output in cups per hour, K is the number of coffee machines (capital), and L is the number of employees hired
per hour (labor).
If Joe’s capital is currently fixed at K=3 machines, what is his short-run production function?
A) q = 3L
B) q = 3L2
C) q = 9L
D) q = 3K2
C) q = 9L
- Technological improvement:
A) can hide the presence of diminishing returns.
B) can be shown as a shift in the total product curve.
C) allows more output to be produced with the same combination of inputs.
D) All of the above are true
D) All of the above are true
- In a certain textile firm, labor is the only short-term variable input. The manager notices that the marginal
product of labor is the same for each
unit of labor, which implies that:
A) the average product of labor is always greater than the marginal product of labor.
B) the average product of labor is always equal to the marginal product of labor.
C) the average product of labor is always less than the marginal product of labor.
D) as more labor is used, the average product of labor falls.
E) there is no unambiguous relationship between labor’s marginal and average products.
B) the average product of labor is always equal to the marginal product of labor.
- Marginal product crosses the
horizontal axis (is equal to zero) at the
point where:
A) average product is maximized.
B) total product is maximized.
C) diminishing returns set in.
D) output per worker reaches a maximum.
E) All of the above are true.
B) total product is maximized.
