Isoquant When Inputs Are Perfect Substitutes

4.1.3. Production with two variable inputs

If all input factors are reduced to two factors, labor and capital, then changing both factors indicates that the enterprise is producing in the long run. The production function in this case has the form: Q = f(K; L)

Isoquant

An isoquant is a curve that shows all the different combinations of inputs that produce a given amount of output.

For example, suppose there is data on labor and capital usage of a business as follows:

Table 4.2: Production with 2 variable inputs

1	2	3	4
1	15	20	30	49
2	20	40	50	79
3	30	50	79	82

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Each number in Table 4.2 is the maximum output that the firm can produce with a given combination of labor and capital inputs. The Q1 isoquant ( Figure 4.3) measures all the combinations of inputs that can produce 20 units of output. For example, 2 units of capital and 1 unit of labor produce 20 units of output, and for the same number of outputs we have a second combination, 2 units of labor combined with 1 unit of capital. Each horizontal row represents the increase in output as the labor input increases (with the capital input being fixed). Similarly, each vertical row represents the increase in output as the capital input increases (with the labor input being fixed).

Q 2 = 50

Q 1 = 20

0 1 2 3 L

Figure 4.3: Isoquant

- Meaning of isoquant: Isoquant shows the flexibility that firms have in making production decisions. In many cases, firms can achieve a particular output by using different combinations of inputs.

As a business manager, one must know the nature of that flexibility in choosing input factors to minimize costs and maximize profits, while paying attention to the law of diminishing marginal productivity.

- Characteristics of isoquant lines:

+ The isoquant lines do not intersect.

+ The farther the isoquant is from the origin, the greater the output level.

+ Sloping downward to the right it shows how one input can be substituted for another input while keeping output constant. This rate of substitution is called the marginal rate of substitution.

Marginal Rate of Technical Substitution (MRTS)

Marginal rate of technical substitution of capital and labor: to reduce 1 unit of labor, how many units of capital are needed with the condition that Q remains constant and vice versa: to reduce 1 unit of capital (K), how many units of labor (L) are needed with the condition that Q remains constant.

The marginal rate of technical substitution is called the slope of the isoquant and is given by the formula: MRTS L/K = - (  K/  L)

Or: MRTS L/K = - (  K/  L) = MP L / MP K (1)

The (-) sign allows to achieve an expression that is always positive.

- We can prove the relationship between MRTS and MP (prove formula 1):

We have: MRTS is closely related to the marginal products of labor MP L and of capital MP K . To see how closely related this is, let us imagine that some labor is added and some capital is withdrawn to keep output constant.

- The additional output resulting from increased labor use is equal to the additional output per unit of labor added (the marginal product of labor) multiplied by the additional labor used.

 Q L = MP L *  L (From the formula MP L =  Q )

 L

Similarly, the reduction in output due to a reduction in capital is the output lost due to a unit reduction in capital (the marginal product of capital) multiplied by the number of units of capital invested.

reduce:  Q K = MP K *  K (From the formula MP K =

 Q )

 K

Since we keep output constant by moving along the isoquant, the total change in output must be zero.

Or we have: MP L *  L + MP K *  K = 0 Therefore: MP L /MP K = - (  K/  L)

Thus, the marginal rate of technical substitution is also the ratio between the marginal product of labor and the marginal product of capital.

This equation shows that: as we move along the isoquant and continually replace capital with labor in the production process, the marginal product of capital will increase and the marginal product of labor will decrease. The combined effect of these changes is that MRTS gradually decreases as the isoquant becomes flatter.

Two special cases of isoquants:

Case 1 : When the inputs are completely substitutes for each other.

When inputs are perfect substitutes, the isoquant is a straight line, and MRTS is constant at every point on the isoquant. That is, the same output can be produced with only labor or only capital, or with a combination of labor and capital.

Example of operating a toll booth:

0 L

Figure 4.4: Isoquant when inputs are perfectly substituted

For the same level of output, it is possible to produce almost entirely using capital alone - using automatic toll collection machines (point A); using labor alone (using people to collect tolls - point C); or using both capital and labor (using both capital and labor to collect tolls at the same time - point B). Thus, at points A and C, capital and labor are complete substitutes for each other.

Case 2 : Input combination ratio remains constant.

In this case, no one input can be substituted for another. Each level of output requires a particular combination of capital and labor. No additional output can be produced without adding both capital and labor in a particular proportion. Hence, the isoquant is L-shaped.

Example of television program production at a television station:

K Development path

manufacture

Q 3

B Q 2

A Q 1

0 L

Figure 4.5: Isoquant with two perfectly complementary inputs

We see that the production of a television program may require a certain combination of capital (cameras, sound equipment, ...) and labor (actors, managers, ...) to produce more television programs, all production inputs must be increased proportionally. In particular: It is difficult to increase capital to replace labor because actors are indispensable inputs for production (except for animated films); at the same time, it is also difficult to replace capital with labor because film production today requires very sophisticated filmmaking equipment.

Points A, B, C are the most efficient production points of input factors. If capital is fixed at K 1 , then increasing labor will not change output or vice versa.

Isocost line

An isocost curve is a curve with the same cost of combining inputs in different ways at a given level of technology.

With total cost C to hire labor at price (wage) PL / unit and capital at price PK / unit, we have:

C = K * P K + L * P L => K = C/P K - (P L /P K ) * L

The above equation is the isocost line equation, with the slope PL / PK .

Optimal choice point when combining input factors

- When combining different input factors, the cost will be different. But there are some combinations that have the same cost.

- When combining isoquant lines with isocost lines, we see that some isoquant lines are tangent to some isocost lines, the tangent points of these lines are the optimal choice points when combining input factors (K; L) when producing the same level of output. At these points, the production cost to produce the product is the lowest. If the selling price of the product does not change, then at the points of combining K and L, the business's profit will reach the highest level. (E) is called the optimal choice point or also known as the point of minimizing production costs.

KC/P K

0 C/P L L

Figure 4.6: Isoquant, isocost and optimal choice point

The set of optimal choice points is the business development path at different scales at different choice levels.

At the same time, at those points, the slope of the isoquant line (MRTS) = Slope of the isocost line or MP L /MP K = P L /P K or MP K /P K = MP L /P L . This is the rule for choosing the optimal input of the enterprise when using 2 inputs K and L.

4.2. COST THEORY

In the production of goods with the participation of many economic sectors and operating according to the market mechanism under the management of the State, enterprises always have to face competition. To win in competition when participating in the market, the important issue that any enterprise must pay attention to is reducing production costs because reducing one dong of cost means increasing one dong of profit. Moreover, manufacturers will decide to produce and consume a certain product depending on the cost and selling price of that product. Therefore, the cost issue is not only a concern of manufacturers but also of consumers and of society in general. So what is the cost to produce goods and services? How will it change when the output level changes? Does the productivity scale of the enterprise affect the cost? We will clarify these issues in the theory of production costs.

4.2.1. Cost classification

According to economist N. Gregory Mankiw: The cost of something is what you have to give up to get it.

In business: Production costs are the total expenses that a business must spend to produce a product in a certain period.

Production costs are a measure of the level of production management organization, an effective competitive tool and the basis for making decisions to achieve the profit goals of the enterprise.

- Accounting costs and economic costs:

+ Accounting costs (current costs): In the production and business activities of an enterprise, costs are often understood as the costs in money that the enterprise spends to produce and do business in a certain period. These costs are recorded in accounting books and are called accounting costs. Accounting costs are costs that the enterprise must spend money on, which can be recorded on the basis of documents.

According to the current accounting regime, cost elements include: Cost of purchased raw materials; labor costs; depreciation; cost of purchased services; other costs in cash.

+ Economic costs:

Economists view costs differently than accountants. For economists: Economic costs include accounting costs and opportunity costs.

Opportunity cost (hidden cost): is all the other things that must be given up to get it.

For example: A private business owner uses his savings of 10,000 USD to buy an old manufacturing facility from another owner. If he did not decide to do so, he could have deposited this money in the bank to earn interest at 10% and he would have received 10,000 USD in income. This means that in order to own this manufacturing facility, he had to give up 10,000 USD in income each year, the 10,000 USD lost each year is one of the hidden costs in this owner's business activities.

Economists and accountants treat costs differently, and this is especially true when it comes to the cost of capital. Economists consider the $10,000 in interest income that the owner forgoes each year to be a cost of his business. But accountants do not, because the $10,000 is not a cost because no money leaves the business to pay for it.

Thus, the important difference in economic analysis between accountants and economists is: Economists are interested in both accounting costs and opportunity costs when calculating the production costs of enterprises. Accountants, who work on monitoring the cash flows in and out of enterprises, only consider explicit costs and often ignore implicit costs (opportunity costs).

To understand better, let's study the following example:

For example: A student after graduating from the Faculty of Economics and Business Administration did not apply to a government agency but instead established a clothing tailor shop. To sew 15 sets of clothes/day, he had to spend 2.5 million VND, including rent, machine depreciation, labor costs and fabric purchase. We call that accounting cost. We see:

This calculation does not take into account the salary of this student. Let's assume that he does not open a tailor shop but works in a state agency, his salary is 30 thousand dong per day, and this 30 thousand dong in the previous chapter we called opportunity cost, here it can be considered as hidden cost.

Thus, economic cost; in addition to the calculation cost, it includes opportunity cost. In this example, the economic cost for 15 sets of clothes is: 2.5 + 0.03 = 2.503 million VND.

In addition, we need to distinguish between sunk costs: expenses that have already been made and cannot be recovered.

Sunk costs are irrecoverable, so they should not be allowed to influence business decisions.

For example, a business is considering moving to a new location in a new city. Last year, the business spent $500,000 to acquire a building in that city. The building was valued at $5,000,000, and the total cost would have been $5,500,000 if the business had actually purchased the building. This year, the business discovers that there is a building in the same city that is worth $5,250,000. Which house should the business decide to buy? The answer is the original house. The $500,000 spent to acquire the building is sunk and should not influence the business’s current decision. The economic cost of the initial building to the firm is $5,000,000 (since this $500,000 sunk cost is just for buying the house and cannot be used for anything else, the opportunity cost of this cost = 0, so it is not an economic cost), while the economic cost of the second house is $5,250,000. Of course, if the second house costs

$4,750,000 should buy it and forgo your option.

The difference between sunk cost and opportunity cost: opportunity cost is what we give up when we decide to do one thing instead of another. Whereas sunk cost cannot be avoided, no matter what our choice is. Because it cannot be avoided, we ignore it when making decisions about various aspects of life, including business strategy.

- Short-term costs and long-term costs:

Short-term costs are costs associated with short-term production and business processes. Long-term costs are costs associated with long-term production and business processes.

4.2.2. Short-run production costs

- Total cost (TC): is the total market price of input factors used to produce the product.

For example, the production of children's clothes. For simplicity, we only consider the following resources, including: factory, sewing machine, fabric and labor. Suppose to produce

Producing 15 sets of children's clothes per day requires 1 sewing machine, 1 worker and 75m of fabric. The factory is rented by the enterprise under a contract, the market price of each factor is determined as follows:

Input

Price (1000 VND)
Factory for rent	100
Sewing machine depreciation	20
Labor	10
Fabric	115
Total cost	245

Thus, to produce 15 sets of children's clothes per day, the business must spend 245,000 VND . However, this total cost will change once the output level changes. However, not all costs increase with output. People distinguish between two types of costs: Fixed costs (FC) and variable costs (VC).

+ Fixed costs (FC): costs that do not change when output changes.

In the above example: factory rent, sewing machine depreciation are fixed costs.

According to the above example: FC = 100 + 20 = 120 (thousand dong)

By extension, fixed costs are costs that a business must pay even if it does not produce any products.

For example: A vendor rents a stall at the market for 5 years. Whether he sells his goods or not, he still has to pay the rent for that stall.

The total fixed cost curve is shown on the graph as a horizontal line, parallel to the x-axis (Figure 4.7).

FC VC TC

Figure 4.7: Shape of FC, VC and TC curves

0 Q