Chapter 6 - Production

Question 1

What are the steps in understanding decisions of a firm?

Answer 1

3 steps:

1) Production technology
2) Cost constraints
3) Input choices

Production technology refers to a practical way of describing how a firm can take inputs (raw materials, labor, capital) and transform it into output. Firms produce different levels of output by using inputs. Keyword here is how the technology of the firm transforms the inputs to outputs.

Cost constraints refer to the price of the inputs such as labor, capital and raw materials. Firms naturally want to minimize the costs.

Input choices refer to “given the production technology and the constraints regarding inputs, the firm must choose how much of each input to use in order to create some level of output”.

These three steps are the building blocks of the theory of the firm.

Question 2

name some inputs that firms use to create output

Answer 2

labor, capital, raw materials

Question 3

What is the production function?

Answer 3

A productions function indicates the highest possible output, q, that is attainable from a combination of inputs.

To simplify our analysis, we use only two types of inputs, while in reality, inputs can be vast.

q = F(K, L)

Output is a function of capital and labor.

The key part about the production function is the fact that it applies for a specific technology. A given set of knowledge about the various methods. AS the technology becomes more advanced, the production function will change. This means that as the technology improved, the same set of inputs can create a larger output than before.

Question 4

What assumption is made regarding the production function?

Answer 4

We assume that the firm runs efficiently, using each combination of inputs as effectively as possible.

Question 5

Why are we interested in short term vs long term?

Define long term and short term.

Answer 5

Because it is difficult to change capital for labor and vice versa in the short run. Changing of machinery etc can easily take up to a year.

When we differ between short run and long run we are essentially splitting up the case in regards to inputs by considering if they can be easily changed or not.

Short run is defined as a time period where the quantities of one or more inputs of production cannot be changed. It does not, however, say that all inputs must not be able to change. Therefore, in the case of q = F(K, L), is K is fixed and labor is variable, we are considering the case as a short run case.

The long run on the other hand is defined as a situation where both inputs/all inputs are considered variable.

Question 6

Given constraints on the possibility of changing inputs or not, what does this do to short term decisions?

(ignore)

Answer 6

As a firm, we can vary the intensity of which we are using current plants etc.
In the long run, we can vary the size of the plant.

Question 7

Consider the case where capital is fixed. How can a firm increase output?

Answer 7

By increasing the amount of labor. The key is to understand how much labor one need to add in order to get a specific level of output. In other words, we need to know the production function.

Question 8

What is average product of labor?

Answer 8

Average product of labor is the average output per unit of labor. In other words, the average product of labor is equal to total output divided by the total amount of units in the labor force of the firm.

Average product of labor = q/L

Question 9

What is marginal product of labor?

How can we find the marginal product of labor, given a production function?

Answer 9

Marginal product of labor refers to the additional output we get by increasing labor by 1 unit.

Marginal product of labor = delta q / deltaL
Could also use differentials

Question 10

What happens to the average product of labor if the marginal product of labor is above it in terms of curves?

Answer 10

If the marginal product of labor curve lies above the average product of labor curve, it means that adding another worker to the labor force of the firm will increase the average product of labor.

Question 11

What happens to the average product if the marginal product curve lies beneath the average product curve?

Answer 11

Adding another worker will drag the average product down. This cause the average product to decrease.

Question 12

When is the average productivity of labor at its highest?

Answer 12

The average product (of labor) is at the highest point when the marginal product curve intersect the average product curve.

Question 12

If we have the function for total product/total output, how do we find the marginal product?

Answer 12

Differentiate the bitch

Question 12

Elaborate on the law of diminishing marginal returns

Answer 12

The law of diminishing marginal returns is saying that as the use of an input increase when other inputs remain fixed, the resulting additions to output will eventually diminish.
Keyword: Eventually. it might first go up, but at some point it will go down and not come up again.

IMPORTANT: This law applied when one variable is subject to move while the others are fixed. IF all variables were to change, say proportionally, this would actually become a returns to scale problem. Therefore, we can say that increasing all inputs proportionally may mitigate the effect of this law, perhaps even removing it.

For instance, when the labor input is small, an additional unit of labor can make big difference. However, if we have 1000 units of labor, adding one more is probably not going to do AS MUCH AS BEFORE.

Worth noting: The law of diminishing marginal returns is not because of labor quality decreasing. It is because of limitations of things like machinery and plant. In other words, the law of diminishing marginal returns is a result of the fixed variable, capital in this case.

the law of diminishing marginal returns applies to a given production technology.

NB: Diminishing marginal returns does not mean negative returns. It can come to such point, too many chefs in small kitchen for instance, but in general this is not the immediate case.

Question 13

how can more output be produced from the same sizes of inputs?

Answer 13

Improve technology

Question 14

How can a total output curve make it look like there are no diminishing marginal returns, when there are in reality?

Answer 14

If the technology improves while there really is diminishing marginal returns, then the technology improvement can dominate the diminishing marginal return, making it seem like there is none.

Remember that the output function has output on vertical axis and input of ONE type on the x axis.

Question 15

What is the difference between total output and total product and total productivity?

Answer 15

There is no difference, they are used interchanably.

Question 16

If you have the total product/total output curve, how do you find the average product of labor (or some other input)?

Answer 16

We draw a line from origin to the point of interest. The slope of the drawn line will be equal to the average output/product per labor.

Keep in mind that this requires the output function to have output on one axis and some input, labor for instance, on the other. This of course means that we are considering a case where only one of the inputs are subject to change (typically the short run)

Question 17

When we regard production with two VARIABLE inputs, what assumption is made?

Answer 17

We are in the long run now, considering the fact that both capital and labor are variable.

Question 18

What is an isoquant?

Answer 18

an isoquant is a curve that shows all possible combinations of two inputs that yield the same output.

this assumes that labor and capital in fact can reach the same output with different values.

Question 19

What is the point of isoquants?

Answer 19

The isoquant map and individual isoquants shows a firm its flexibility in terms of business decisions. We can use the different combinations yield by an isoquant to figure out the cost-optimized way of running things.

It is essentially a tool that helps us understand decisions. For instance, it shows how increasing only one input is doomed to deliver decreasing efficiency in the long run. Therefore, the appropriate solution is probably to increase all inputs at a good proportional rate. Note that proportional rate does not imply that they are on the same level. It means maintaining a certain ratio between inputs: Ex 1 unit of labor per 1 unit of machine etc.

Question 20

What is MRTS?

Answer 20

MRTS is marginal rate of technical substitution. It is obtained by finding the slope of the isoquant and removing the negative sign. It is basically exactly the same as MRS. Like the MRS, MRTS is always measured in positive quantity.

For instance: MRTS is the rate at which we can substitute units of capital (y axis input) for 1 additional unit of labor (x unit input)

Question 21

What do we mean by tabulating inputs?

Answer 21

Tabulating the inputs is possible when we are using only 2 inputs. We create a table showing the different combinations of inputs and the output they (together) yield.

Question 22

what is the point of isoquants?

Answer 22

Isoquants are first and foremost a tool that helps us understand how production work. Different combinations of inputs can yield the same output.
Also, as we increase on of the inputs while the other inputs remain constant, we can see how the marginal returns diminish.

Question 23

The marginal rate of technical substitution is equal to the ratio of marginal productivity of labor divided by marginal productivity of capital. What does this mean? How do we get to this result?

Answer 23

It means that the rate of which we need to consider to add more labor at the cost of reducing capital while keeping the output constant is equal to the ratio of marginal productivity of labor and marginal productivity of capital.

We find this result by considering a small movement along the isoquant curve and considering that this needs to be equal to 0.

Question 24

Name the extreme cases of the production function. Elaborate on both of them

Answer 24

The production function that shows perfect substitutes and perfect complements are considered the extreme cases.

Perfect substitutes are referring to inputs that can be used interchangeably without impacting production/output. This means that capital can be traded for labor without second thoughts. The result is isoquant curves that are linear and with slope -1.

The other case is often called Leontief production function. Perfect complements. In this case, we cannot make any substitution between the inputs. This means that every level of output requires a specific combination of inputs. The result is L shaped isoquant curve. These curves are also called fixed-proportions production function.

Question 25

What can we do to increase output?

Answer 25

Increase both inputs

Question 26

Define returns to scale

Answer 26

Returns to scale refer to the rate at which production/output increase in regards to proportional increases on inputs.

There are 3 scenarios possible in regards to returns to scale.
1) Increasing returns to scale. Increasing inputs lead to even bigger increase in return to scale
2) Constant.
3) Decreasing returns to scale.

Question 27

What is increasing returns to scale?

What could cause it?

Answer 27

Increasing returns to scale refer to the scenario where, for instance, doubling the inputs lead to more than doubling of the output.

Could be caused by specialization. Allows use of assembly lines. Standardization. Up to a certain point at least.

If you have increasing returns to scale, it would be economically beneficial to create a large factory rather than having many small.

Question 28

What is constant returns to scale?

What could cause it?

Answer 28

For instance, output will double if inputs are doubled.

If our firm has constant returns to scale, it does not matter if we build larger or several small units.

Question 29

What is decreasing returns to scale?

What could cause it?

Answer 29

If doubling the output requires more than doubling of the inputs.

What this means is that it will be more EFFICIENT to run several smaller joints that to focus on a big one.

Complexity and difficulties in regards to running a large organization could be a reason for decreasing returns to scale. Actually, decreasing returns to scale is most commonly a result of communication and coordination problems, and organizational problems.

Question 30

Find first order conditions of average product of labor, q/L. Elaborate on the result

Answer 30

dq/dL = (dq/dL * L - q*dL/dL)/L^2 = 0

1/L(dq/dL - q/L) = 0

So, either 1/L is 0, or dq/dL - q/L = 0

dq/dL = q/L

this result means, the average product of labor is GREATEST when it is equal to marginal product of labor.

Question 31

Elaborate on returns to scale. How do we figure out whether a firm has increasing, decreasing or constant returns to scale?

Answer 31

We look at its production function. It is all about whether a proportional increase in inputs lead to a larger increase in outputs, smaller or constant.

In special cases, the production function is not enough to find returns to scale. In such cases, we find the optimal point of production, and use this point as a reference for further analysis. For instance, Leontief.