Chapter 7 - Cost of production

Question 1

Define accounting cost

Answer 1

Accounting cost is the actual expenses plus depreciation for capital equipment periodized

Question 2

Defiene economic cost

Answer 2

Cost to a firm of utilizing economic resources in production. Forward looking.

Economic costs are those costs that are relevant to a certain decision.

Question 3

Elaborate on opportunity cost

Answer 3

The cost of using something in regards to its best alternative usage. For instance, a building could be leased instead of being used for office etc.

Question 4

What is the most important thing about opportunity cost and economic cost?

Answer 4

Forward looking. Always in the future.
Decisions based: Always relevant for the decision to be made.

Question 5

Define marginal costs:

Answer 5

The additional cost of producing 1 additional unit.

MC = deltaVC/deltaq = deltaTC/deltaq

MC = dVC/dq = dTC/dq

Question 6

Define average cost/average total cost

Answer 6

Average cost is the total cost of production divided by the amount of units in output. Gives the average cost per unit produced.

AC = TC/q

AC has two components;
1) AVC
2) AFC

In all cases, average costs, total costs, variable costs, fixed costs, are usually given as dollars per year or something similar.

Question 7

What’s important to consider regarding fixed costs when seen in a long run perspective?

Answer 7

In the long run, all costs are variable.

Question 8

How can we develop marginal cost to include wages?

Answer 8

The point here is that when we have only one variable input, we can quickly define the marginal cost.
The marginal cost is equal to the price of that variable input unit, divided by the marginal productivity of that input.

MC = priceOfinputUnit / MP_{inputUnit}

If the variable input is labor, then we have the following:

MC = w / MP_{L}

Assume we talk about units of labor in hours. Let us say the price of one unit of labor is 30 usd. That takes care of the w.
MP_{L} = change in output divided by change in labor. Meaning, the additional output we get for an additional unit of labor. Let us say one unit of labor gives us output of 10 (additional output). Then the marginal cost is equal to 30/10 = 3. This is basic shit. This is the marginal cost! Remember that marginal cost is the additional cost required to create/produce one additional unit. When we added the labor unit of 1 hour, this unit gives us 10 units extra output. We need to accommodate for this and get the shit over at the form of cost per additional OUTPUT.

Cost of producing one more output-unit is equal to the price of one extra input-unit divided by the amount of extra output-units this extra input-unit delivers.

EXTRA FORMULATIONS: NOT UPDATED; NOT SURE HOW GOOD

Recall that marginal cost is the additional cost required to produced one more unit. If we look at labor as the only way of regulating output, we can consider this: fixed wage w, change in labor dL.

MC = dTC/dq (Change in costs per change in output)

MC = dTC/dq = dVC/dq (VC = TC because fixed costs are not relevant in marginal costs)

MC = dVC/dq = w(dL/dq), because wdL = dVC

MC = w*(dL/dq) = w * MP_{L}^(-1)

MC = w/MP_{L}

Meaning, the marginal cost (additional cost of 1 more unit) is equal to the wage divided by the marginal productivity of labor, which is the additional output we get by adding one more unit of labor. The larger the output per labor is, the lower the marginal costs will be. If the output per labor is really small, the marginal costs will be huge.

This is essentially just a way of saying that the cost of producing one extra unit is dependent on how much output the extra labor needed will deliver.

ADDITIONAL EXPLANATION; NOT SURE HOQW GOOD

Marginal cost is the additional cost to produced one more unit.
This additional cost must be variable. If we assume the firm can hire as much labor as it wants to fixed wages “w”, then deltaVC = w*deltaL

MC = dVC/dq = w*dL/dq

MC = w/MP_{L}

In other words, the marginal costs is equal to the wage divided by the marginal productivity of labor

Question 9

Why does a firm have more flexibility in the long run than in the short run? I am thinking in regards to actual real life things

Answer 9

In the long run the firm may change machinery, buy new equipment, expand contract and initiate new ones etc.

Question 10

What is the “user cost of capital”

Answer 10

Annual cost of owning and using a capital asset. Equal to economic depreciation + interest rate*ValueOfCapital.

Interest rate is because of the fact that this money could be used to earn interest instead.

Question 11

What is the “rate” per dollar of capital?

Answer 11

r = depreciation rate + interest rate

Depreciation rate is the rate of depreciation (Lmao) meaning how fast it depreciates. If we buy a plane that we believe will last 30 years, the depreciation rate is 1/30 = 3.33 percent.

Interest rate is whatever rate we could get on our money elsewhere. Let us say we can get 10% elsewhere.

Therefore, our rate would be equal to 3.33 + 10 = 13.33%.

This rate is an opportunity cost rate, and you’ll have to compare this percentage for all alternatives to figure out whether the cost of capital is good or not. You’d want to pick the lowest, because that one offers the best revenue to cost ratio.

Question 12

When we are trying to figure out how to select inputs to produce a given output at minimum cost, what do we work with in terms of inputs?

(ignore)

Answer 12

We consider labor in hours and capital in hours of machine time.

Question 13

Define isocost line

Answer 13

An isocost line shows all possible combinations of inputs that can be purchased for a given total cost.

C = wL + rK

We can rewrite this like we do with the budget line:

K = C/r - (w/r)*L

This is obviously a linear curve with intercept C/r and slope -w/r

Question 14

How do we choose inputs to produce at some output level at minimum cost?

Answer 14

The intersect point (only one, not two) where the isoquant curve representing a level of output interests an isocost line will represent the point where the cost-minimized combination of inputs are. If the output level is import, we adjust the isocost line by shifting it until we reach the tangency point. If the budget is most important, we figure out where the isoquant curve is that intersects the isocost line at only one point. This yield the best use of our inputs.

If the level of output is most important, then use the isoquant curve that shows all combinations yielding this number of output. Then we enter the isocost line and shifts it until it intersects the isoquant line in exactly one point and stands tangent. At this point we know that we have used the lowest possible isocost line to produce the specific output.

If the budget is more important, we use the isocost line to show our furthest budget, and then find the isoquant curve that intersects isocost in only one point.

Question 15

Elaborate on the expansion path of a firm

Answer 15

The expansion path is a tracer curve that shows the cost-minimized combination of inputs for each level of output. Therefore, this path is the best path to choose input combinations from.

The expansions path is a curve that trace the points where an isoquant intersect an isocost curve at exactly one point. Therefore, the expansion path shows the best / cost minimized option, or cost minimized combination of inputs, for each level of output. In other words, the expansion path shows the combinations of labor and capital that the firm will choose to minimize its costs at each output level.

the expansion path shows the firm what it has to set its inputs to if it wants to get output to a certain level.

Question 16

What is the cost curve/long run cost curve?

How is it created?

Answer 16

The long run cost curve is a curve that shows the cost associated with different levels of output.

We can create it by using the expansion path.

Question 17

How do we go from the expansion path to the long run cost curve?

Answer 17

3 step method.
1) Choose an output level represented by an isoquant. then find the point of tangency of that isoquant with an isocost line.

2) From the chosen isocost line, determine the minimum cost of producing the output level that has been selected.

3) Graph the output-cost combination.

This is basically just: For each point on the expansion path curve, figure out what the output level is (isoquant) and what the cost is (isocost). Then we can plot this tuple up in a separate plot that maps output values to costs.

Question 18

What is the difference between short run and long run? This chapter talks about short run costs and long run costs as if they are different things? What is the difference, and what is its implications?

Answer 18

The difference is the short run inputs are split into variable and fixed. IN our case, since we are considering only 2 inputs, one of them will be variable and the other will be fixed. Therefore, we need to separate these costs when doing decisions, as the variable costs are the only ones of interest (assuming the timeframe of interest is too short to consider doing anything about the fixed costs).

In long run problems, both costs (in our case with 2 inputs) are variable. This means we can make decisions that doesn’t involve separating the type of cost.

Question 19

What is the difference between marginal returns and marginal cost?

Answer 19

Marginal returns refer to the additional OUTPUT we get by adding one more unit of input. This is dependent on the marginal product(ivity) of labor (or some other input that is variable).

Marginal cost refer to the additional COST required to produce one more unit of output.

Question 20

What happens to marginal cost when marginal return diminish?

Recall that marginal returns is equal to the additional return in output associated by adding one unit of some input, while keeping the other units fixed. For instance, adding one more unit of labor.

Answer 20

The key to understanding this is to reflect on the difference between marginal cost and marginal productivity of labor (or another input). Marginal productivity of labor is the additional output associated with adding another unit of labor. The wage, w, of labor, does not reflect the cost of adding another output, but the cost of adding another unit of labor. To find the marginal cost, we need to figure out how much this wage rate actually contributes with, but dividing it by the number of added outputs the extra labor unit increase the total output level with.

First of all, marginal returns diminish as a result of diminishing marginal productivity of labor (or some other variable input). Diminishing marginal productivity refers to the fact that as we add more and more units of some input, the effect of adding one more becomes smaller and smaller. When this happens, the marginal cost will actually increase. MC will increase because due to the lower effect of each additional unit of input, we have to pay more per extra input to get the same level of output. You could say that as the marginal productivity of labor decrease, it becomes more expensive to buy extra output using this specific input. Therefore, the marginal cost increase as marginal productivity decrease.

Question 21

How do we measure labor in long run decisions?

Answer 21

We use the wage rate, w. Typically per hour.

Question 22

How do we measure capital in long run decisions?

Answer 22

Unlike as it is with short run decisions, now (in long run) we can actually change the input size of capital. Therefore we must place a price on it.

The important thing is that capital is not money, and capital includes every asset that can yield money/value in other usages. Most assets are not yet sunk costs. We can still utilize them in some ways.

We want to express capital as dollars per year, as a FLOW, even though capital is not only money. In order to do this, we must amortize the spending by spreading the “cost” over the lifetime of the capital. We must also take foregone interest into account.

This is exactly what we do when we calculate the user cost of capital. Depreciation rate + interest rate

IMPORTANT: This is the price of capital, not the size of capital. It is the “r”, just like the “w” (wage rate) is the price of labor.

Question 23

What is the price of labor?

Answer 23

Wage rate

Question 24

What is the price of capital?

Answer 24

User cost of capital, r

Question 25

What happens to the cost of capital if we rent the asset of interest?

Answer 25

Then the price of capital becomes the rental rate. However, in a competitive market, the rental rate will be approximately equal to the user cost of capital anyways.

Question 26

Compare short run to long run production in terms of flexibility. Consider increasing outputs in both cases. What happens?

Answer 26

We know that in the long run, both input factors are variable. This allows us/the firm to do more planning and be flexible. Therefore, we can use both capital AND labor to meet our goals.

However, in the short run case, we can only use flexibility in terms of labor to meet our desired level of production output.

What does this imply?
It is all about the isoquants and isocost curves. Reflect on what they look like.

If we can only use labor to meet the desired output, and capital is fixed, we would have to move horizontally until we meet the isoquant that represent our desired level of output. The key thing here is that since capital is fixed, we cannot choose the cost minimized point/combination of inputs. Therefore we have to pay the price of inflexibility by buying shit loads of labor. This is not good for us because of the low of diminishing returns (marginal productivity of labor will diminish).

If we consider the case of long run, we can be perfectly flexible in regards to combinations of inputs. Therefore, in the long run, we can pick the cost-minimized point. this point is the one where MRTS is equal to the slope of the isocost curve/line.

Question 27

What is the short run expansion path?

Answer 27

A horizontal or vertical straight line that shows us that when one input is fixed, we dont have much choice/flexibility if we want to increase output.

Question 28

Define economies of scale

Answer 28

We use the term economies of scale when doubling the output requires less than doubling the cost.

The effect of this is that: As output increases, the average cost of producing that output will decrease, at least to a certain point.

MAKE NO MISTAKE IN CONFUSING ECONOMIES OF SCALE WITH RETURNS TO SCALE.
Economies of scale is all about how the average cost of producing will decline when output increase. This means that a doubling of output will require less than a double of cost.

On the other hand, returns to scale is all about how output change as ALL inputs receive a proportional change.

Question 29

Define diseconomies of scale

Answer 29

We say diseconomies of scale when doubling the output requires more than doubling the cost.

Question 30

As output increases, the firms average cost is likely to decrease, at least to a certain point. Why is this likely?

Answer 30

As output increase, the firm will get a “bigger” business. This allows workers to specialize. Managers can organize more effectively.

The firm can buy in huge quantities at reduced price.

Question 31

At some point, it is likely that the average cost of production will increase as output increase. Why is that? We have previously assumed that it is the opposite up until this point?

This is a long run question

Answer 31

Factory space and machinery may be overcrowded.

Huge organizations can offer extremely complex environments.

In certain special situations, the firm might be so big that buying all the supplies it needs becomes difficult because of shortages.

It can be tempting to relate diseconomies of scale to the law of diminishing marginal returns, but this not entirely correct. That law is a short term concept. Diseconomies of scale is a long term concept. The law of diminishing marginal returns assumes all but one input are fixed. Diseconomies of scale does not do this. This allows the law to not really apply in the same away as in short run.

Question 32

What can you use cost-output elasticity for?

Answer 32

cost-output elasticity can be used to measure economies of scale or diseconomies of scale.

Cost output elasticity is the percentage change in cost of production that will result from a 1-% change in output.

Ec = deltaC/deltaQ / (C/q) = MC / AC

WHen marginal cost is greater than average cost, adding a unit of output will drag the average down, which implied diseconomy of scale. If marginal costs are lower than average cost, then the cost-output elasticity will be lower than 1, and we are in an economy of scale.

Question 33

Elaborate on the product transformation curve

Answer 33

The product transformation curve is a relationship between several products produced in-house.

If the firm operates under an economy of scope, this curve will bend down and will be round.
If no difference, the curve will be a flat line.

If there is a diseconomy of scope situation, the curve will be convex.

Question 34

Define economies of scope

Answer 34

Economies of scope refer to the case where joint output of a single firm is greater than the output that could be achieved by two separate firms producing a single product.

Question 35

Define diseconomies of scope

Answer 35

Diseconomies of scope refer to the case where a firms joint output is smaller than that which could be achieved by two separate firms producing a single product.

Question 36

Elaborate on the “degree of economies of scope”

Answer 36

The degree of economies of scope refer to the percentage of cost production is saved when two products are produced jointly rather than individually.

SC = ( C(q1) + C(q2) - C(q1, q2)) / ( C(q1, q2) )

If SC is greater than 0, then we have economies of scope.
IF SC is smaller than 0, then we have diseconomies of scope.

Question 37

What is meant by the “learning curve”?

Answer 37

The learning curve refers to the fact that the different parts of the firm, especially parts involving humans, tends to learn as time pass by. The learning effect cause higher productivity. This leads to lower average cost.

The learning curve effect makes it look like a growing firm is just experiencing increasing returns to scale. Recall that increasing returns to scale describe a situation where doubling all inputs lead to more than a doubling in output. In reality, the firm might just be learning, and not really be subject to increasing returns to scale.

The learning curve plot the amount of inputs needed to produce an output unit to its cumulative output. Meaning, on the horizontal axis, we have cumulative output. On the vertical axis, we have the number if input units, ex hours of labor, required.

As the cumulative value increase, the number of input units required to create/produce a single unit decrease. Therefore, the curve takes the same shape as indifference curves, sort of, considering they look like the exponential distribution.

Formally, the learning curve follow this relationship:

L = A + BN^{-beta}

N is the cumulative output
L is labor per unit of output
A, B and beta are constants with B and A positive, and beta between 0 and 1.

Question 38

Define the mathematical learning curve function and explain the parts

Answer 38

L = A + BN^(-beta)

L equals the measure of time required or inputs needed in order to create one unit of the output.

A equals the intercept. Would be the time required or inputs needed to create the very first unit of product.

B equals some slope factor.
N is the variable, representing the cumulative output.

beta is a constant.

A, B, beta are all constants. A and B must be positive, and beta must be between 0 and 1.

This means, the larger the beta, the more important the learning effect is.

Question 39

What is user cost of capital?

Answer 39

User cost of capital aims to capture the effect of using capital. It goes like this:

UserCostOfCapital = Depreciation of the asset we are considering + forgone interest

We could also say per dollar, r = depreciation rate + interest rate

Therefore, user cost of capital measure what we are giving up, typically on a yearly basis, to use that particular asset.