TOPIC 6 ► COST THEORY

LEARNING OUTCOMES

By the end of this topic, you should be able to:

1. Describe several concepts of economic costs;
2. Draw the curves of short-run costs;
3. Explain the curves of short-run costs;
4. Relate the  short-run costs with the long-run costs; and
5. Evaluate why the long-run average costs curve has a U-shape.

INTRODUCTION

In Topic 5 we discussed the choices faced by firms in solving the question of how outputs should be produced. When firms make decisions regarding the production techniques and combinations of inputs used, we know that the firm operating the production process obtains its supply of inputs from households or other firms. Inputs have to be paid for according to the market price which is determined in the input market. The payment made is cost for the firm. The costs involved in production will change according to the amount of output. We all have our own understanding about the definition of costs. However, costs that we normally define only involve private costs and accounting costs. The concept of costs in economics is more extensive where economic costs involve all tangible and intangible costs. In this topic, we will discuss the concept of costs in economics before discussing further regarding the short-run and long-run production costs.

6.1 CONCEPT OF COST

Generally, costs are matters that must be exchanged or sacrificed in order to obtain something else in return. The sacrifice made can involve various forms, which can be valued monetarily or not. Costs may be in the form of money, goods, time and so on.
Firms must know the shape of the cost curves in order to make decisions. Short-run costs curve is used to make decisions regarding output and price; while long-run costs curve is used for growth planning and investment policy.

6.1.1 Economic Costs

Economists consider all costs of inputs used in production without taking into account who owns the inputs. This view influences their definition towards costs, profit and optimal production level.
You have been exposed to the concept of opportunity cost in our discussion about the production possibilities curve. The concept of opportunity costs is the basis of the concept of economic costs.

Economic costs for a good can be defined as the value of the best alternative foregone in order to obtain the particular good.

Therefore, to determine the economic cost of a certain good, economists must calculate the sacrifices that have to be made by the society in order to produce one additional unit of that particular good. Figure 6.1 illustrates the components of economic costs.

Figure 6.1: Components of economic costs

ACTIVITY 6.1

How do we apply the principle of opportunity cost towards a particular firm? Discuss.

6.1.2 Private Costs and Social Costs

Private cost is the cost that has to be paid by an individual who is directly involved in the production or consumption of a particular good.

Social cost or external cost is the cost burden carried by individuals who are not directly involved in the production or consumption of that particular good.

Let us take the process of cooking oil production from oil-palm trees as an example. Private costs are costs that have to be paid by the manufacturer to the supplier of raw oil-palm, labour force, amount of electricity used and others.
However, this factory may produce industrial wastes that can pollute the river or drainage systems nearby.
This pollution problem might cause some members of the society living around the area to lose their source of income or their recreation area. Meanwhile, the government is forced to use tax revenue money to clean up the pollution. All these costs are considered as external costs or third-party costs. In this case, the social cost is higher than private cost.
External costs are caused by external effects. Since external effects can be negative or positive, external costs can also reduce or increase social costs. Positive external effects such as the joy experienced by society from the scenery of a private garden, causes the private cost borne by the garden owner to be higher than the social cost. This is because society benefits from that garden. 

6.1.3 Explicit Costs and Implicit Costs

Economists have divided private costs into explicit (tangible) costs and implicit (intangible) costs.

Explicit cost is the market value of all inputs purchased by a producer.

Implicit cost is the market value of inputs owned by the producer himself.

Self-owned inputs of the producer are such as the value of his own building used, and the expertise possessed by the producer. Self-owned resources are valued based on opportunity cost, that is, value of the best alternative foregone. This implicit cost is the cost that differentiates economic costs and accounting costs or the related concepts, namely economic profits and accounting profits.
To further explain these two concepts, we look at an example:
Assume that you have graduated from OUM and have received a job offer at the value of RM40,000 per annum. But you are determined to start your own business using the money you inherited from your grandfather at the value of RM50,000. At the end of the first year of your business, your accountant showed you the list of expenditure consisting of labour wage (RM50,000), rental (RM18,000) and other costs (RM17,000), which amounted to RM85,000. However, due to sound foundation in the principles of microeconomics, you know that your private cost is much higher.
In your calculation, the implicit cost you have to bear includes the value of the job offered, that is, RM40,000 per annum, and value of the interests from your savings of the inherited money at the rate of 10 percent or RM5,000 per annum. Thus, you add in another RM45,000 into the amount of RM85,000 totalling up the overall private cost to RM130,000.
This concept of economic costs is the one that we will apply in our following discussion on production costs.

ACTIVITY 6.2

Give three examples of implicit costs. Discuss the matter with your friends to broaden your knowledge.

6.2 SHORT-RUN PRODUCTION COSTS

In reference to our discussion on short-run production in Topic 5, short-run production involves the use of fixed inputs and variable inputs. The cost that is related to fixed inputs is referred to as fixed cost, while cost related to variable inputs is the variable cost. Now, let us look at the definition of fixed costs and variable costs.

Fixed costs are costs that do not change according to change in output.

Variable costs are costs that change along with the change in output.

When we only use two types of inputs in the short-run, that is, capital as the fixed input and labour as the variable input, hence, rental for capital is the fixed cost and payment of wage for labour is the variable cost.

6.2.1 Total Cost

Total cost of a firm is the economic cost of the firm. Total cost (TC) comprises the total fixed costs (TFC) and the total variable costs (TVC) or:

Total Cost	=	Total Fixed Costs + Total Variable Costs
TC	=	TFC + TVC

If r is rental for one unit of capital (K), and capital is the fixed input, hence, fixed cost is r × K; and if w is wage for one unit of labour (L), while labour is the variable input, then variable cost for one production level is w × L. Since variable cost will change along with the change in output, we state the variable cost as a function to output, for example TVC = 2Q. Therefore, you will obtain the function of total cost such as TC = 1000 + 2Q, where 1000 is TFC and 2Q is TVC. Indirectly from here we will obtain:

Total Fixed Cost	=	Total Cost – Total Variable Cost
TFC	=	TC – TVC

and

Total Variable Cost	=	Total Cost – Total Fixed Cost
TVC	=	TC – TFC

Table 6.1 and Figure 6.2 illustrate the three types of total costs. Total fixed cost and total variable cost are calculated based on the assumption r = RM25 per unit of capital, and w = RM10 per unit of labour.

Table 6.1: Total Costs
 

Figure 6.2: Total cost curve, total fixed cost curve and total variable cost curve

Observe that the total fixed cost curve is horizontal because fixed cost does not change along with the change in output. Meanwhile, the total variable cost curve increases at an increasing rate (curve becoming steeper) due to the law of diminishing returns in short-run. The total cost curve is the vertical sum of fixed cost and variable cost. Therefore, the distance between the total cost curve and the total variable cost curve (a) represents the total fixed cost.

6.2.2 Average Costs

Average Fixed Cost (AFC) is the total fixed cost divided by total output, or

Average Fixed Cost = 
or AFC = 

If TFC = 1000, hence AFC = 1000/Q
Average Variable Cost (AVC) is the total variable cost divided by total output, or:

Average Variable Cost = 
or AVC = 

If TVC = 10Q, then AVC = 10Q/Q = 10
Total Average Cost (AC) is the total cost divided by total output;

Total Average Cost = 
or AC = AFC + AVC

Average cost can also be computed by adding average fixed cost and average variable cost.
From the example above, hence AC = (1000/Q) + 10.

6.2.3 Marginal Costs

Marginal cost is the change in total cost caused by one unit of output change, or:

Marginal Cost = 
or MC = 

Total costs consist of total fixed costs and total variable costs. However, since only the total variable cost changes along with the change in output, hence marginal cost can also be obtained from the following equation:

Marginal Cost = 
or MC = 

Now, refer to Table 6.1 for the calculation of AFC, AVC, AC and MC; and Figure 6.3 for the drawing of AC, AFC, AVC and MC curves.

Figure 6.3: Average cost and marginal cost curves

Observe that the average fixed cost will continually decline but does not reach zero due to the value of fixed cost divided by the total output that is increasing. Meanwhile, the average variable cost decreases a little at a lower level of output, but then increases due to the law of diminishing returns. Meanwhile, total average cost is the vertical sum between average fixed cost and average variable cost. Due to the continually decreasing average fixed cost, the distance between AC and AVC becomes narrower when output increases.
AC decreases longer than AVC because initially, the decreasing effect of AFC is bigger than the increasing rate of AVC. After one point, the increase in AVC gives a bigger effect compared to the decrease of AFC. AVC and AC are normally U shaped because the average cost usually decreases in the beginning but increases after one point due to the law of diminishing returns.
Marginal cost (MC) decreases along with AVC at the early stage of production but increases after one point due to the law of diminishing returns. MC and AVC are equal at the first output level. MC intersects AC and AVC at the minimum point of AC because if marginal or addition is lower than average, average will decline; but if addition is higher than average, average will increase. The relationship between MC and AC is similar to the relationship between marginal and other averages, that is, average cost will increase if marginal cost is higher and the contrary if marginal cost is lower than average cost.

Relationship between Production and Short-Run Costs

What is the relationship between production and short-run costs? Production involves the purchase of inputs. Therefore, cost and production have an inseparable relationship. Firms have to know the relationship between these two short-run concepts especially for the purpose of determining the output level in the short-run. Hence, here we will try to look at the relationship between short-run average cost and marginal cost, with short-run average product and marginal product.
The connection between short-run cost and short-run production can be described as the following:
Assume you have just opened a tailoring shop that receives orders to sew dresses. Workers are the variable inputs and the shop is a fixed input. Here we will only look at the productivity of the variable inputs. When you hire a worker with a wage of RM10 per hour (w = RM10) and the worker is able to complete sewing 2 dresses in an hour, the total variable cost for 2 dresses is RM10
(TVC = RM10) and:
Average variable cost, = AVC =  =  = RM5
Average product for the worker AP =  =  = 2
From here we are able to see the connection between AVC and AP, that is:
AVC =  =  = RM5
AVC =  can also be stated as AP = w/AVC.
Due to increasing orders, you will hire another worker with the same amount of wage, that is, RM10 (w = RM10) per hour. Both workers are able to complete 6 dresses in an hour. Hence, the marginal product is:

While marginal cost is:

We see that RM2.50 can also be obtained from w/MP. Therefore, we obtain the relationship between MC and MP, that is, MC = w/MP or MP = w/MC. AP and AVC for both workers are AP = 6/2 = 3, and AVC = w/AP = RM10/3 = RM3.33. We find that AVC declined from RM5 to RM3.33, and AP increased from 2 to 3.
From the relationship that we have just described (AVC = w/AP), we can summarise that when AP is maximum, then AVC is minimum, and vice-versa. Also, because MC = w/MP, hence MP is maximum when MC is minimum, and vice-versa.
The relationship between both the two cost curves and two production curves can be seen clearly in Figure 6.4, that is, the average cost curve and marginal cost curve are the mirror images for the average product and marginal product.

Figure 6.4: Relationship between cost and production in short-run

ACTIVITY 6.3

Try to give other examples you have came across to establish the relationship between cost and production in short-run.

6.3 LONG-RUN PRODUCTION COSTS

In the previous section, we have looked at the concept of cost in the short-run and its importance in the decision-making of firms in the short-run. Even though the discussion only involved variable inputs but the conclusion obtained can be applied in productions using more than one variable input, and at least one fixed input.
Firms will continue to be in the short-run situation as long as production involves fixed cost. When a firm alters its operation size by transforming fixed input into variable inputs, then the firm will be in the long-run situation and facing long-run costs.
Long-run costs and short-run costs are different due to a number of reasons:

1. There are no fixed costs in the long-run. Hence, TC = VC;
2. The law of diminishing marginal returns does not occur in the long-run because the firm is able to change all inputs. Therefore, the law of diminishing marginal returns does not influence the long-run costs curve;
3. The size of plant and production level change continuously along the      long-run costs curve because all inputs are variable. Therefore, the long-run costs curve shows the minimum production cost for every output level when all inputs are variable;
4. Producers cannot build a plant that is tandem with the long-run average costs curve (LAC). This is because each plant built has its own short-run costs; and
5. Long-run is also the planning period for a firm. If demand is found to be increasing, the producer will plan to increase production by building or upgrading their production equipments. If demand is found to be insufficient, the firm can pull out from the industry.

6.3.1 Average Costs and Marginal Costs in the Long-Run

Long-run average cost is also known as the planning curve because it depicts a growth path that can be followed by the firm only in the long-run.

The average cost and marginal cost in the long-run are U-shaped due to different effects of returns to scale at different level of outputs.
Figure 6.5 illustrates the long-run total cost (LTC) and the long-run average cost (LAC) that faces three conditions of economies of scale at different levels of output. The curve shows an increasing return to scale or economies of scale at the initial output level to Q1, while production from Q1 to Q2 depicts the constant returns to scale. After Q2, the firm faces diseconomies of scale.

Figure 6.5: Long-run average cost curve and long-run marginal cost curve

Curve LAC is constructed based on a few assumptions:

1. Input price is fixed in the market. Therefore, change in input price involves change in cost and causes the LAC curve to shift upwards or downwards;
2. The technology and quality of inputs are constant and may only change in a very long period of time; and
3. The firm chooses a combination of lowest cost for every level of output. Therefore, besides LAC, the optimization rule MP_A/P_A = MP_B/P_B = …. = MP_N/P_N has been fulfilled. If the firm does not choose the optimal combination, production is located at a point on LAC, not along LAC.

6.3.2 Economies of Scale

Earlier, you have come across the phrases economies of scale, diseconomies of scale and constant economies of scale. Now let us look at the explanation for each of these concepts.

1. Economies of Scale We can see that long-run average cost (LAC) is U-shaped similar to the short-run average cost (SAC) but more gently sloped. Some writers refer to it as saucer-shaped. The U-shape of LAC is caused by scale economics or economies of scale. If you still remember, the U-shape of short-run average cost curve is due to decreasing returns.
   
   Economies of scale can be caused by increasing returns to scale and also other factors. Firms facing economies of scale will find a continuously declining LAC curve.
   
   Figure 6.6 illustrates the long-run total cost and average cost curves facing economies of scale.
   
   

   

   Figure 6.6: Long-run total cost curve and average cost curve for economies of scale

   Economies of scale or economies of production on large scale explain the reasons why LAC declines. The decline in LAC with the increase in plant size can be caused by many factors. We will look at some of these factors.
   

   

   Figure 6.7: Factors influencing the decline of LAC

   
   Let us go through each factor:
   1. Labour Specialisation Labour specialisation can be increased when the size of plant increases. When more workers are hired then it would be easier for them to perform more specialised tasks
   2. Efficiency of Management Efficiency of management can be achieved when the size of plant increases and managers can increase efficiency by managing more workers and more materials.
   3. Efficiency of Equipment Usage Sometimes machines are operated below its true capacity if the plant is small. When the size of plant increases, usage of capacity can be increased.
   4. Reduction in Input Cost When materials are purchased in large quantities, the firm may obtain a higher discounted rate. Large firms are able to purchase raw materials at lower prices compared to small firms. Hence, production cost can be reduced.
2. Diseconomies of Scale
   Diseconomies of scale occur when the firm operates at the right side of minimum point of LAC, where LAC is increasing. Diseconomies of scale can be caused by decreasing returns to scale or other factors including:
   1. Inefficiency of management that might be caused by increase in bureaucracy, or excessive burden to the management. Hence, cost increases.
   2. Increase in input cost. This can happen when many firms simultaneously increase their capacity which causes the input price to increase due to competition.
   Figure 6.8 illustrates the long-run costs curves for diseconomies of scale.
   
   

   

   Figure 6.8: Diseconomies of scale

3. Constant Economies of Scale Besides economies of scale and diseconomies of scale, long-run production may also face constant economies of scale. Constant economies of scale can be caused by constant returns to scale, that is, when output increase is equivalent to input increase. The LAC for this condition is horizontal as shown in Figure 6.9.

Figure 6.9: Constant economies of scale

SELF-CHECK 6.2

Can you identify the position of Figure 6.6, Figure 6.8, and Figure 6.9 in Figure 6.5? If you can, try to explain in your own words about each situation that makes the LAC U-shaped as in Figure 6.5.

6.3.3 The Relationship between Short-Run Costs and Long-Run Costs

We know that before making any investment decisions, entrepreneurs are in the long-run situation because they can choose among the alternatives shown by the levels of technology. When decisions have been made and fund is tied to fixed capital, they start operating in the short-run. Therefore, short-run costs and     long-run costs have certain relationships.
The two basic relationships between long-run costs curve and short-run costs curve are:

1. Long-run cost is less than or equivalent to short-run cost for every production level [(LTC (Q) ≤ STC (Q) for all levels of Q)].
2. Long-run cost and short-run cost must be equal on at least one level of output.
   1. Relationship between the Long-Run Total Cost and Short-Run Total Cost A long-run total cost curve of a firm at one particular level of output is the total cost related to the combination of minimum input cost that can be used to produce the level of output. Therefore, the long-run cost curve is the envelope for short-run cost curve, that is, each point on the long-run cost curve is tangent to a point on a short-run cost curve.
      
      For example, from Figure 6.10, with the size of plant represented by STC₁, the firm achieves minimum cost when Q₁is produced. With that, STC₁ and LTC are equal at that particular level of output. Meanwhile, when the size of plant is increased to STC₂, cost is optimal at Q₂, hence, STC₂ and LTC are equal at that particular output level. The same goes for all other sizes of plants. When the size of plant can be changed continuously, countless of the amount, hence a smooth LTC curve is formed as we can see in Figure 6.10.
      
      

      

      Figure 6.10: Short-run total cost curve and long-run total cost curve

      For a firm facing constant economies of scale with a horizontal LAC, the short-run total cost curve and long-run total cost curve is as shown in Figure 6.11. Observe that the short-run optimal output is always equivalent to the long-run optimal output.
      

      

      Figure 6.11: Short-run total cost curve and long-run total cost curve for constant economies of scale

   2. Long-Run Average Cost and Short-Run Average Cost
      From the relationship between STC and LTC as shown above, the relationship between long-run and short-run average costs and marginal costs, can be illustrated as in Figure 6.12.

      

      Figure 6.12: Short-run costs and long-run costs

      Meanwhile, for a firm facing constant economies of scale, the average cost curve is horizontal because the optimal point of short-run average cost is always equivalent to long-run optimal cost. In this condition, any level of output, and any plant size is considered as the optimal size. The LAC curve for constant economies of scale is shown in Figure 6.13.
      

      

      Figure 6.13: Long-run costs curve of constant economies of scale

      From what we have seen, the long-run average cost (LAC) curve is the envelope to an amount of short-run average costs (SAC). Each point on LAC touches one point on one SAC related to one plant size. Figure 6.14 illustrates several SAC of various plant sizes for the firm facing a U-shaped LAC. Observe that when LAC decreases, that is, at the left side of point A, the LAC touches the left side of SAC where the short-run cost is decreasing and vice-versa at the right side of A. LAC only touches the minimum point of SAC at the minimum point of LAC.
      

      

      Figure 6.14: Short-run average cost curve and long-run average cost curve

      Through the SAC curves, we can see that size gives the lowest production cost for one output tier. If a firm wants to produce as much as Q₁ units, hence the firm will use the first plant size. If a firm wants to produce Q₂ unit, the optimal size will be the second plant due to a lower average cost compared to the first. If the first size is used for Q₂output, average cost is Q₂B but if the second plant is used, average cost will be Q₂A. But if the firm is not able to change the size to plant 2, being in the short-run, cost Q₂B has to be borne. However, the optimal size of plant is size 3 because minimum point of SAC touches the minimum point of LAC.
   3. Long-Run Marginal Costs and Short-Run Marginal Costs Long-run average cost is the envelope for short-run average cost, but on the other hand, long-run marginal cost is not the envelope for short-run marginal cost, SMC. However, LMC is equivalent to SMC when LAC is equivalent to SAC. This is because when SAC = LAC, it means that the short-run total cost is equivalent to the long-run total cost (STC = LTC). We know that SMC is the gradient of STC, and LMC is the gradient of LTC. Therefore, when STC = LTC, then SMC = LMC. Look at points A and A’, and points M and M’ in Figure 6.14.
      
      However, SMC = LMC = SAC = LAC at only one point, that is, the minimum point of LAC. The marginal cost intersects with the average cost at the minimum point of average cost, thus when LAC achieves the minimum point, hence LMC = LAC, and when SAC is minimum, SMC = SAC. Therefore, what we can conclude that the optimal point in the long-run is achieved at LAC = SAC = LMC =  SMC.

SUMMARY

• Economic costs consist of private costs and social costs.
• Private cost is the cost borne by the producer, while social cost is the cost borne by the society.
• Private costs consist of explicit costs and implicit costs.
• Explicit cost is the tangible cost such as payment to production factors purchased in market, while implicit cost is the cost for inputs owned by the producer.
• Short-run total production cost consists of total variable costs and total fixed costs. When total cost, total fixed cost and total average cost are divided by total output, average cost, average fixed cost and average variable cost will be obtained.
• Meanwhile, marginal cost is the addition in cost caused by an addition of one unit of output.
• Short-run average cost and short-run marginal cost are mirror images to the short-run average product curve and short-run marginal product curve.
• Firms operating in long-run can choose the optimal capacity from various sizes of plants.
• Therefore, the long-run average cost curve is the envelope for the short-run average cost curve.
• Firms operating in long-run may be facing economies of scale, constant economies of scale, and diseconomies of scale.
• One of the factors that influence economies of scale is the returns to scale.