UGBA 101A Week Five & Six: Production

Question 1

The production decisions of firms can be understood in three steps

Answer 1

Production Technology
Cost Constraints
Input Choices

Question 2

Production Technology

Answer 2

How inputs (such as labor, capital, and raw materials) can be transformed into outputs

Question 3

Cost Constraints

Answer 3

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.

Question 4

Input choices

Answer 4

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

Question 5

Theory of the Firm

Answer 5

Explanation of how a firm makes cost-minimizing production decisions and how its cost varies with its output

Question 6

Why do Firms Exist?

Answer 6

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.

Question 7

How do firms avoid individual bargaining?

Answer 7

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

Question 8

What 3 categories can factors of production be divided into?

Answer 8

Labor
Material
Capital

Question 9

What does a Production Function show?

Answer 9

• 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

Question 10

What do production functions describe?

Answer 10

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

Question 11

Short Run vs Long Run for the Production Function

Answer 11

• 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

Question 12

Average product

Answer 12

output per unit of a particular input

Question 13

Marginal product

Answer 13

additional output produced as an input is increased by one unit

Question 14

average product of labor =

Answer 14

output/labor input = q/L

Question 15

marginal product of labor =

Answer 15

change in output / change in labor input (change q / change l)

Question 16

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?

Answer 16

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)

Question 17

can the average and marginal product curves intersect?

Answer 17

yes

Question 18

When the marginal product is above the average product, is the average product increasing or decreasing?

Answer 18

when the marginal product curve is above the
average product, the average product is increasing.

Question 19

When the marginal product is below the average product, is the average product increasing or decreasing?

Answer 19

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.

Question 20

When total output is maximized, what is the marginal product?

Answer 20

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!

Question 21

What is the marginal product beyond the maximum total product point?

Answer 21

negative

Question 22

In general, how do we determine the average product of labor at any one point?

Answer 22

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.

Question 23

In general, how do we determine the marginal product of labor at any one point?

Answer 23

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)

Question 24

The Law of Diminishing Marginal Returns

Answer 24

The principle that as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease

Question 25

How to calculate labor productivity?

Answer 25

Output per unit of labor

Average product of labor for an entire
industry or for the economy.

Question 26

How can labor productivity increase?

Answer 26

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

Question 27

Consumers in the aggregate can increase their rate of consumption in the long run only by increasing the _________ they produce

Answer 27

total amount

Question 28

Stock of capital

Answer 28

total amount of capital available for use in production

Question 29

technological change

Answer 29

development of new technologies allowing factors or production to be used more effectively

Question 30

What do isoquants curve show?

Answer 30

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.

Question 31

What do isoquant maps show?

Answer 31

Isoquant maps are graphs combining a number of isoquants, used to describe a production function

Question 32

What describes the firm’s production function?

(production with two variable inputs)

Answer 32

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

Question 33

By drawing a horizontal line at a particular level of capital for an isoquant map, what do we observe?

Answer 33

diminishing marginal returns

in figure 5.5, we can observe that each additional unit of labor generates less and less additional output

Question 34

How do isoquants show input flexibility?

Answer 34

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.

Question 35

How does diminishing marginal returns apply to production with two variable inputs?

Answer 35

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

Question 36

What is the marginal rate of technical substitution (MRS)?

Answer 36

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)

Question 37

Diminishing MRS

Answer 37

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

Question 38

How are isoquants shaped?

Answer 38

downward sloping and convex (like indifference curves)

Question 39

What does the slope of the isoquant at any point measure? What ability of the firm is this?

Answer 39

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

Question 40

What is the special case of production function: fixed proportions production function? (or Leonitief production function)

Answer 40

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.

Question 41

What situations does the fixed-proportions production function (Leonitief production function) describe?

Answer 41

The fixed-proportions production function describes situations in which
methods of production are limited

Question 42

What is the special case of production function when the isoquants have inputs that are perfect substitutes?

Answer 42

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)

Question 43

Does adding one variable alone in the case of fixed proportions production function increase output?

Answer 43

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

Question 44

returns to scale

Answer 44

rate at which output increases as inputs are increased proportionally

Question 45

increasing returns to scale

Answer 45

situation in which output more than doubles when all inputs are doubled

Question 46

constant returns to scale

Answer 46

situation in which output doubles when all inputs are doubled

Question 47

decreasing returns to scale

Answer 47

situation in which output is less than doubled when all inputs are doubled

Question 48

Do returns to scale need to be uniform across all possible levels of output?

Answer 48

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

Question 49

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

Answer 49

larger

Question 50

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

Answer 50

equally spaced (6.3)

Question 51

when there are increasing returns to
scale as shown in (b), the isoquants ______ as inputs are increased along
the line.

Answer 51

move closer together (6.3)

Question 52

How does a long-run production function differ from a short-run production function?

Answer 52

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.

Question 53

Why is the marginal product of labor likely to increase initially in the short run as more of the variable input is hired?

Answer 53

Initially, adding more workers allows individuals to specialize.

Question 54

What is the difference between a production function
and an isoquant?

Answer 54

An isoquant shows different combinations of inputs at a specific output level, while production functions show different outputs with maximizing combinations.

Question 55

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?

Answer 55

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.

Question 56

Can an isoquant ever slope upward?

Answer 56

No – output would change but it is fixed in an isoquant

Question 57

Explain the term “marginal rate of technical substitution.” What does a
MRTS = 4 mean?

Answer 57

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.

Question 58

What does a MRTS = 4 mean?

Answer 58

You can increase one unit of an input (labor) for 4 units of a currently used input (capital).

Question 59

1. 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

Answer 59

C) q = 9L

Question 60

2. 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

Answer 60

D) All of the above are true

Question 61

3. 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.

Answer 61

B) the average product of labor is always equal to the marginal product of labor.

Question 62

4. 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.

Answer 62

B) total product is maximized.