ABSE 203 - FIT



ABSE 203 PRODUCER DECISION MAKING

Production and costs

1. The firm and its motivation

The firm is at the center of the study of microeconomics. It is the economic agent that directly makes decisions what to produce, how to produce, and for whom to produce. In this course we will concentrate on the decisions that firms make.

The first point of our analysis is the motivation of the firm? Why do firms make one or another decision? What do they want to achieve? Economists can discuss many different goals that firms may set for their operations – to sell as much as possible (maximize sales) and gain a greater market share, to satisfy customers and gain social prestige, to become better than competitors, to increase production steadily and protect environment, etc. All these goals could not be achieved, however, if the firm does not make profits, or if it loses money.

In this course we will take profit maximization as the primary and only firm’s goal.

One does not need going to school to figure out that profit (Π) is the difference between total revenues (TR) and total costs (TC), or

Π = TR – TC

Therefore, in order to study the decisions of the firms, we have to concentrate on the analysis of costs.

2. Costs and expenditures

First, we have to make a difference between COSTS and EXPENDITURES.

We study aggregate expenditures in macroeconomics. They presented the demand side of the economy. Here we will study costs that present the supply side of the economy. While the reduction in aggregate expenditures is a warning factor and at the moment the economy is slowing down due to the sharp fall in expenditures, the decrease in costs is the best news for business. This means that firms can produce more with the same resources, or that they can produce a good or service with fewer resources.

Shortly, costs are the money paid for the factors of production. This is the most general meaning of costs, BUT it is not quite correct from the perspective of business and economics. When we report costs in our accounting records, such an understanding of costs is right, but when we assess the economic profitability of the firm, it does not work out.

3. Accounting and economic costs

Accountants keep a record of costs because they have to justify the firm’s operations and the taxes that are paid to the government and to the municipality. Since there is always an opportunity to cheat and report more cost and less profit in order to pay less taxes, the government can check accounting papers of firms. This is why accountants keep documents for every payment that the firm has performed and give these documents as an evidence for the firms’ costs. Therefore, we can conclude that from the point of view of accountants costs are the money paid for the factors of production. In other words, accounting costs are all the costs that have documental evidence and that are recognized by the taxation officers. These are costs that have been explicitly paid and we call the EXPLICIT costs.

If, for example, a firms has paid €1 000 for production (raw materials, wages, electricity, etc.) and it has made €1 010 total revenues, its profit is €10 and it will even pay to the government €1.50 taxes on this profit. From the accounting point of view the firm is profitable and its profit is €10. However, one does not need going to school to figure out that this business does not make any sense, because it is not profitable – the rate of profit is just 1%, while the firm could have had more ( say, 2%) if it would just have had put the money into a bank, instead of running such a business.

This example presents the importance of opportunity costs in economic decisions. Actually, putting money in a business means that the owners lose the interest that could have been earned from a bank. Therefore, from economic point of view, this interest that is lost is a cost of doing business. It is the opportunity cost of capital and should be compensated by the revenues of the business. If it is not, then the business is losing money. It is not profitable. Therefore, the economist will consider this money lost and a cost of business. It is not explicit cost, because it has not been actually paid, but it is a cost. We call it IMPLICIT COST. Thus, from the point of view of economics, we consider not only explicit costs of the firm, but implicit costs, as well.

Economic costs = explicit costs + implicit costs

One example of implicit costs is the interest on the money, invested in the firm, that could have been earned at zero risk elsewhere (from a bank deposit, or from a government bond). Another example of implicit cost is the salary that the owner of the firm could have earned elsewhere, if he were working for someone else instead of working for his own firm. Another example is the rent that the owner of the firm could have get from renting out the shop (if he owns it) instead of making business in it.

Let’s solve the following problem:

One year ago, Tom and Jerry set up a vinegar bottling firm (called TJVB).

■ Tom and Jerry put €50,000 of their own money into the firm. (They used this money to pay for equipment, labor, etc.)

■ They rented equipment for € 30,000;

■ They hired one employee to help them for an annual wage of € 20,000;

■ Tom gave up his previous job, at which he earned € 30,000, and spent all his time working for TJVB;

■ Jerry kept his old job, which paid € 30 an hour, but gave up 10 hours of leisure each week (for 50 weeks) to work for TJVB;

■ The prevailing interest rate was 10%

■ The cash cost of TJVB (for raw materials and like) were € 10,000 for the year.

What is TJVB’s accounting cost and what is its economic cost?

|Explicit costs |30000+20000+10000 = 60000 |

|Implicit costs |30000+10x50x30+10%x50000 =30000+15000+5000 = 50000 |

|Accounting costs |60000 = explicit cost |

|Economic costs |60000+50000=110000 (implicit cost + explicit cost) |

The explicit cost includes all the payments that have been really made – for rented equipment, for the worker’s wage and for raw materials and like. These costs will be recognized by the taxation officer and they are accounting costs.

The economic costs will include not only explicit costs but the implicit costs as well – the interest on capital (10% of €50,000), which is lost, Tom’s salary (€ 30,000), which is lost, and Jerry’s time (which is worth € 30 an hour, 10 hours a week, 50 weeks a year), which is lost too.

4. Economic profit and accounting profit

If TJVB’s total revenues for the year were €100 000, their accounting profit would be TR – accounting costs = €100 000 - €60 000 = €40 000.

However, these €40 000 are not enough to compensate Tom and Jerry for the money lost in this business. If they had not started this business, they would have had more – interest on capital, Tom’s salary, and Jerry’s leisure time which he could use either to make more money, or to do whatever else he would like.

Economic profit = total revenues – economic costs = €100 000 - €110 000 = - €10 000.

Their economic profit is negative. They have economic loss.

If total revenues were €120 000, they would have had €10 000 an economic profit.

What if their total revenues just cover the economic costs? If TR = €110 000, the accounting profit is €60 000, but the economic profit is €0. This means that Tom and Jerry could have made the same money if they would not have started this business. They now make as much as before. Thus, they could have made the same money elsewhere, because it just equals the opportunities lost. Economists say that such a profit is NORMAL PROFIT. It equals the implicit costs.

To Tom and Jerry the business would make sense is they are able to make at least normal profit. In other words, they do not lose anything because they make as much as elsewhere. Their accounting profit equals their implicit costs. Their economic profit is zero. Any accounting profit above €60 000 assures a positive economic profit. Any accounting profit below €60 000, means that the business is not profitable and they’d better not have started this business.

Let’s conclude. The first question that the firm should raise is whether it makes sense at all to start a business. The positive answer depends on the expected profitability of the business. If we may expect at least a normal profit, then the firm is expected to cover its economic costs and starting business is justified.

5. Production function and technological choice

The second problem that the firm has to solve is what technology to use in business. As we know from the very first lecture in economics, technology is a way of putting resources together. It matters for firm’s decisions because profit maximization is a function of output (the more the output, the greater the revenues) and inputs (the cheaper the inputs, the lower the costs).

Therefore the choice of technology depends on the one hand on relationship between the output and inputs and on the other hand on their prices in the market.

Let’s focus on the first factor determining technological choice – the relationship between the output and the inputs. It is presented by the PRODUCTION FUNCTION.

The relationship between the amount of various inputs used in the production process and the level of output is called a production function.

The production function is usually stated mathematically. Then it is a mathematical representation of the relationship:

Q = f (L,N,K)

Output (Q) is dependent upon the amount of capital (K), Land (N) and Labour (L) used.

The meaning of the production function is to help us to find the maximum output that can be produced with given resources. Therefore, technologists are to find the most effective way of putting resources together in order to have maximum output with minimum inputs.

From this perspective we can distinguish between efficient and inefficient technologies. An efficient technology is the one that minimizes the amount of resources for a given output. Therefore, it is impossible to reduce one of the inputs and not to reduce the amount of output. An inefficient technology is the one that does not minimize the amount of resources for a given output. Therefore, it is possible to reduce one of the inputs and not to reduce the amount of output. For example, if in the post office you fire one of the employees and this does not affect the work of the office, so that they still do the same work, the technology in the post office is not efficient. If however, at Frederick, you cut one of the positions of secretaries, you will find out that the amount of work done by the administration will be reduced and the University will not be able to perform its functions appropriately. This means that it is impossible to reduce one of the inputs and to avoid negative effects on the output. Therefore, the technology at the university is efficient.

Watch out! Technological progress constantly affects the assessment of efficient technology. Technological methods that have been efficient yesterday might be inefficient today. This is why economists and technologists use the production function to improve the organization of production.

Production functions describe only efficient levels of output; that is, the output associated with each combination of inputs is the maximum output possible with that set of inputs, given the existing level of technology. Production functions change as the technology used in the production process changes.

The second factor that affects technological choice are the prices of inputs. A technology with more modern machines and less labor might be more progressive from engineering perspective, but it might be more expensive per unit of output produced. Therefore, firms would prefer a more labor intensive technology that is cheaper per unit of output.

The firm hires one more worker because it expects this worker to contribute to the increase in output. Otherwise it will not waste its money and pay this worker for nothing. Therefore, the utility that the firm gets from the workers is measured by the output. The extra utility from an extra worker is the increase in output, created because this extra worker is hired.

The increase in output due to the increase in labor by one unit (hiring one more worker) is called MARGINAL PRODUCT OF LABOR (MPL).

The increase in output due to the increase in capital by one unit is called MARGINAL PRODUCT OF CAPITAL (MPK).

Therefore, the firm makes the best technological choice if it finds a technology where:

MPL/PL = MPK/Pk

Such a choice means that the firm can produce maximum output at minimum cost. This is the least cost production decision.

6. The Law of Diminishing Marginal Returns

The rule for cost minimization sets a new point of analysis. We shell study the dynamics of marginal productivity. Let’s focus on the marginal product of labor (MPL). As we saw it is the increase in output (increase in the total product of labor – TPL) as a result of hiring one more worker (increase in labor).

MPL = ΔTPL/ΔL

Respectively,

MPK = ΔTPK/ΔK (marginal product of capital is the increase in the total product of capital as a result of the increase in capital by a unit).

a) the short run period

If we want to analyze the dynamics of the marginal product of labor, we should study how it will change with the change in the number of workers in the firm, while all other factors are kept constant. (Otherwise, if the other inputs change too, we cannot know which one contributed more to the change in output). Moreover, this fits the actual situation in the firms. At any given moment, there is at least one factor of production that does not change with the output. For a given period it is fixed and does not depend on output. Such a period in production is called a SHORT RUN period. In the short run there is at least one fixed factor of production. No matter what happens in production, this factor does not change. The firm can increase or reduce production, but this factor will stay fixed. Respectively, the cost of this factor is FIXED COST. A typical example of fixed cost is the rent for a building, office, equipment, etc. The firm signs a contract for renting the building and until this contract expire, it has to be paid, no matter whether the firm produces more, or less, or even zero output. Another example of a fixed cost is the interest paid to the bank on a loan. These fixed costs have to be paid and therefore they set a constraint on firm’s decisions, because they are out of its control. When the contract expire, the short run period is over. Then the firm is free to make any decisions – to renew the contract, to close the business, etc.

We will analyze the dynamics of the marginal product of labor in the short run. The fixed factor is capital. We will change only the number of workers, but everything else will stay fixed. Further, we will assume that all workers are equally good for the job and work equally well. Let’s take an example for better understanding.

Assume that Petros decides to open a bakery in a new neighborhood in Limassol where developers have built a lot of new houses but no shops and bakeries. Petros rents a small place and starts his business with just one worker. The worker produces 15 kilos pitas a day. People in the neighborhood like very much pitas and are ready to buy more. Petros hires a second worker. Workers start specializing in different operations and as a result the bakery produces 32 kilos pitas a day. Output increase by 17 kilos. The marginal product of labor MPL = 17. The demand for pitas is still higher and Petros hires a third worker. Now they produce 57 kilos pitas a day. The MPL = 25. The business is so successful that Petros hires a fourth worker. The output now is 80 kilos. The MPL = 80 – 57 = 23 kilos. The increase in output however is smaller than before. 2319). Why? Look at the numbers. When Petros hires the fourth worker, the law of diminishing marginal returns starts operating and the MPL falls from 25 to 23 kilos. The output increases by 23 kilos. Before (when there were only three workers) the APL was 19. Now TPL increased by 23. It does not matter that the increase is slower than before, but that 23 >19. If the increase is greater than the average, the average will rise.

Look now at the case when Petros hires the fifth worker. The MPL is only 15. TPL rises by 15, but the average product before hiring this worker was 20. Now the increase is smaller than the average (15 APL, the APL increases. When MPL < APL, APL falls. The APL neither falls, nor increases when MPL = APL. Thus, the APL is maximum at the intersection of the two curves.

7. Long run decisions

If Petros finds out that the demand for his pitas will keep growing, he might think of expanding his business. When his contract for the shop rented expires, he can think of renting a bigger shop, or of renting two small shops. Now he does not have any more any fixed costs and he can change the scale of production. This is a LONG RUN period – there is no fixed costs. All costs are variable.

While in the short run costs depend on the law of diminishing marginal returns, in the long run the problem that has to be soled is whether to produce in one big shop (factory), or in two or three small shops (factories). This is the problem of the scale of production. It is a function of technology. In some industries, we can observe production taking place in very big factories (automobile production, electrical power plants), while in some others production is organized on a much smaller scale (bakeries, restaurants). Firms choose the scale of production on the basis of productivity. If with a larger scale of production productivity rises faster and respectively costs per unit fall, the firm prefers a bigger factory to a smaller one. If it is the other way round – productivity falls with the increase of the scale of production and respectively the costs per unit increases, firms prefer a smaller scale of production. Therefore, the choice of scale of production depends on the RETURNS TO SCALE (RS). They are calculated as a ratio of percentage change in output to percentage change in production factors.

RS = % change in the output : % change in production factors

If RS > 1, output rises faster than the increase in capacity. The firm enjoys economies of scale. Then, it will prefer a larger scale of production.

If RS < 1, output does not increase as fast as the capacity of production and the firm suffers diseconomies of scale. Then production will be organized in smaller units.

If RS = 1, the increase in output is proportional to the increase in capacity. In this case it is all the same whether the firm will build one big factory, or two or three small factories.

Thus, the choice of production capacity is a long run decision and it depends on the returns to scale.

8. The costs of the firm

a) short run costs

When the firm has chosen the technology, it starts producing. The decision period is short run. Some of the production factors are fixed (for example, the chosen equipment) and respectively, some costs are fixed. This period will end when the firm’s contracts expire.

At the same time, in the short run the firm has to decide how much to produce. If demand for the goods is rising, the firm may increase output. If demand is falling, it may reduce it. This means, that the firm will buy more or less raw materials, electricity, labor, etc, depending on the demand. The cost of these resources will change with their quantity. These costs are VARIABLE COSTS.

In the short run the firm has two types of costs – fixed costs (FC) and variable costs (VC).

Therefore, in the short run total costs (TC) = FC + VC.

Fixed cost is the cost of fixed factors and they are out of the firm’s control in the short run. This means that if even the firm decides not to produce at all, it still has to pay this cost (for example, the interest on bank loans, the rent for equipment, or for land, etc).

Why a firm might decide not to produce at all and pay only the fixed cost until its contracts expire? If the demand is falling dramatically and the firm is loosing money because it cannot sell its output, it might prefer to minimize losses and reduce output to zero.

In other words, the firm will decide how much to produce on the basis of its profitability. Let’s recall that the goal of the firm is to maximize profits (or, if it is loosing money but cannot – to minimize losses until the short run period expires).

The question is – how much should the firm produce in order to maximize profit? We can find the answer in the analysis of the firm’s costs and revenues.

First, we should remember that in the short run operates the law of diminishing marginal returns. It means that after a particular point the extra cost for an extra unit of output will start increasing.

Extra cost for an extra unit of output is MARGINAL COST.

MC = TCn – TCn-1 units

At the beginning, the increase in output is associates with falling marginal cost because the marginal product of the variable input increases. When the law of diminishing returns starts operating, marginal product begins to fall and respectively marginal costs begin to rise.

Let’s analyze Petros costs of production in the short run. Assume, that Petros has signed a contract for the rent of his shop and for the equipment and he has to pay €10 a day fixed costs. No matter whether he produces zero pitas or 100 kilos, his fixed cost is €10. If he produces more, his variable costs increase. Petros is a very well organized person and he has put his costs on the following table.

|Q |FC |VC |TC = FC + VC |

|0 |10 |0 |10 |

|1 |10 |6 |16 |

|2 |10 |11 |21 |

|3 |10 |14 |24 |

|4 |10 |16 |26 |

|5 |10 |21 |31 |

|6 |10 |27 |37 |

|7 |10 |35 |45 |

|8 |10 |46 |56 |

We can see. That with the increase in output variable costs increase. However, till the 4th unit of output the increase in variable costs is not as fast as the increase in output, while after the 4th unit of output, variable costs start rising much faster. In order to see it in details, let’s find marginal costs and average costs.

Average costs (AC) are costs per unit. Average TC is total costs per unit of output, average FC is fixed costs per unit and average VC if variable cost per unit.

AC = TC/Q

AFC = FC/Q

AVC = VC/Q

When Petros produces zero output, he does not have any marginal or average cost. When he raises output from zero to 1, his extra cost is 6. Therefore, his marginal cost is 6. He produces 1 unit and his total cost is 16. AC = 16. AFC = 10 and AVC is 6. When he raises output from 1 to 2 units, his extra cost is 11- 6 = 5. MC = 5. His AC = 21: 2 = 10.5, AFC = 10: 2 = 5 and AVC = 11: 2 = 5.5. We will present all the costs on the table below.

|Q |FC |VC |TC = FC + VC |MC = ΔTC: ΔQ |AC = TC: Q |AFC = FC:Q |AVC = VC:Q |

|0 |10 |0 |10 | - | - | - | - |

|1 |10 |6 |16 |6 |16 |10 |6 |

|2 |10 |11 |21 |5 | 10.5 |5 | 5.5 |

|3 |10 |14 |24 |3 |8 | 3.3 | 4.7 |

|4 |10 |16 |26 |2 | 6.5 | 2.5 |4 |

|5 |10 |21 |31 |5 | 6.2 |2 | 4.2 |

|6 |10 |27 |37 |6 | 6.12 | 1.7 | 4.5 |

|7 |10 |35 |45 |8 | 6.4 | 1.4 |5 |

|8 |10 |46 |56 |11 |7 | 1.25 | 5.75 |

After the 4th unit of production, the law of diminishing returns starts operating and marginal costs start increasing. Average costs keep falling because MC < AC. When at the 7th unit of production MC becomes greater than the average costs, AC starts rising too. The same rule that we found in the analysis of productivity, holds here. If MCAC, AC is rising. AC is neither falling, nor rising when MC = AC. At this point AC is at its minimum. If we present these costs graphically, the MC curve will intersect the AC curve at its minimum point.

[pic]

Fig. 2. MC and AC. The MC curve intersects the AC curve at its minimum point.

b) firms revenues

The analysis of the firm’s costs reveals that AC is minimized when Petros produces 6 units of output. Thus, an engineer would suggest to produce 6 units of output. However, Petros does not want to minimize costs. He wants to maximize profits! If he has a growing demand and buyers are willing to pay more and more for the pitas, so that they will compensate for the increasing cost per unit, Petros should increase production. This simple logic comes from common sense. Therefore, in order to find the amount of output that should be produced for profit maximization, we have to analyze not only costs, but revenues as well.

Let’s start with a few basic revenues concepts.

Total revenues (TR) are found when we multiply the amount of output sold and the price of the good. Petros produced and sold 5 kilos of pita, €8 each and made:

TR = €8x5 = €40

TR = P x Q

Average revenue is revenue per unit. It is just the price of the good. Petros got €8 per kilo.

AR = P

Marginal revenue is the extra revenue, derived from selling an extra unit of output. Pteros sold the 5th kilo of pita and got €8 more. Before, when he sold 4 kilos, his TR was €8 x 4 = €32. Now his TR is €8 x 5 = €40. His MR = ΔTR : ΔQ = (€40 - €32) : (5–4) = €8.

MR = ΔTR : ΔQ

c) profit maximization decision

In order to find how much should Petros produce in order to maximize profit, we have to compare his revenues and his costs, because profit = TR – TC.

Let’s start with the case when Petros produces and sells 4 units of output (at this point starts operating the law of diminishing returns and Petros’ MC begins to rise). If buyers are ready to pay €8 per kilo of pitas, Petros should compare his extra cost for producing one more kilo of pitas to the extra revenue that he will get from selling the 5th kilo. Take the numbers from the table. In our case, his MC for the 5th kilo is €5, while he can make €8 more from selling it. MR > MC. It make sense to increase production, because he will increase his profit by €8 - €5 = €3.

If MR > MC, the firm is not maximizing profit and it should increase production to add some extra profit.

If, Petros is producing 5 kilos of pita, he is still not maximizing profit, because MR (€8) > MC(€5). If he is producing 6 kilos still MR (€8) > MC (€6). So Petros increases production to 7 kilos. Now MR (€8) just equals MC (€8). If he raises output further – to 8 kilos, his MR (€8) becomes less than MC (€11). The 8th kilo of pita will cost more that buyers will pay for it and Petros will reduce his profit. He will lose from the 7th kilo of pita.

If MR < MC, the firm is not maximizing profit and it has to reduce output.

Therefore, the firm will maximize profit if MR = MC.

This condition (MR = MC) is the first and most important condition for profit maximization. However, it is not a sufficient condition. The firm should be able to cover its average costs. In our case Petros can be happy. The price = €8 > €6.40, what is Petros’ average cost at the production of 7 kilos of pita.

We can now summarize the conditions for profit maximization:

The firm maximizes profit when:

MC = MR and

P > AC

The point where P = AC the firm is just compensated for all its economic cost and therefore it makes normal profit. This point is the break even point.

The firm is breaking even when P = AC.

d) loss minimization decision

What if the price is not covering AC? Let’s assume that Petros is not that happy and his buyers are not willing to pay more than €6 per kilo. In this case, Petros can apply the rule of MC = MR and chose to produce 6 kilos of pita where his MC = €6 = MR. Unfortunately, at this point his AC = €6.12. The price does not cover cost per unit and Petros will loose €0.12 from every kilo sold. Then isn’t it better to stop producing and shut down?

If Petros decides that he is loosing money and he should shut down the business, he will produce zero output, but he will still have fixed cost = €10. In the short run the firm has fixed cost and it cannot control it. Until Petros contracts for renting the shop and the equipment expire, he has to pay the fixed cost. Thus, if he shuts down, he will have a loss of €10 = FC. Then, maybe it is better to consider not shutting down but staying in business and still producing. It will make sense if the loss is less then if he shuts down. If Petros produces 6 kilos of pita, we saw that his loss is €0.12 from every kilo sold. He sells 6 kilos and therefore his total loss is €0.12 x 6 = €0.72. This is much less than €10. He’d better stay in business and produce 6 kilos of pita. His loss will be less than shutting down.

Now we can think of the rule for loss minimization. Since the firm has fixed cost in the short run and this cost is out of its control, when it comes to losses, the firm should consider just the variable cost. If the price is high enough to cover the AVC, P>AVC, then the firm will be compensated for the extra variable cost and there will be still something left to compensate part of the fixed cost. If Petros produces 6 kilos of pita and the price is €6, P > AVC (€6 > €4.50). He is compensated for the variable costs and still has €1.50 (€6 - €4.50) to cover part of the fixed cost that is anyway lost. He is minimizing losses.

The firm minimizes losses in the short run if:

MC = MR and

P > AVC

When P = AVC the loss is exactly equal to fixed cost and it does not matter whether the firm will stay in business, or shut down. If P < AVC, then the firm is losing more than the fixed cost and it is not minimizing losses. Therefore, the maximum loss that a firm shall make in the short run is its FC.

The point where P = AVC is called the shut down point.

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APL

MPL

AC

MC

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