1/11 Chapter 23: Theory of the firm short run costs (1.5) [11 pages] HL extensions Short and long run costs Total cost picture Unit cost picture Linking total product to the unit cost picture Calculating costs Costs of production in the short run Explain the distinction between the short-run and the long-run with reference to fixed costs and variable costs Distinguish between total costs, marginal costs and average costs Draw diagrams illustrating the relationships between marginal costs and average costs, and explain the connection with production in the short run Explain the relationship between the product curves (average product and marginal product) and the cost curves (average variable cost and marginal cost), with reference to the law of diminishing returns Calculate total fixed costs, total variable costs, total costs, average fixed costs, average variable costs, average total costs and marginal costs from a set of data and/or diagrams Short and long run costs Recall that we define the short run as the time period during which at least one factor of production is fixed in the long run all factors are variable. The short run is this rather different for a nuclear power plant and the local bakery. It is worth noting, again, that fixed factors are commonly capital or land and that raw materials and labour are frequently used examples of variable factors. However, there are exceptions! Highly specialised labour such as a nuclear physicist or a master pastry chef might well be fixed factors in the examples above. Thus, any fixed factor will be a fixed cost and the important thing to keep in mind is that in the short run there is at least one fixed cost since one or more factors of production cannot be increased during the period. When we look beyond the short run in Chapter 24, it will become evident that when we are dealing with the time period where any and all factors of production can be changed we are dealing with the long run. The iteration so far has dealt with output as a function of the use of factors in the short run. Firms output
2/11 decisions will be based on translating factor usage into short run costs figures. We commonly use two pictures, i.e. diagrams, to illustrate the costs, the total cost picture and the unit cost picture. Total cost picture in short run (total variable and fixed costs) A firm s total cost picture is given by taking total fixed costs (TFC) and adding the total variable costs (TVC). This gives us total costs (TC). TC = TFC + TVC It is often easier to see the different costs in a table and diagram. Figure 2.3.7 shows output and total costs for the Sturdy-Pants Company as used earlier. The quantity is based on the same weekly output figures for the firm. Note that for me to be able to continue with this example, we must make two assumptions: We will assume that only labour costs are variable. Each unit of labour costs $500 per week. All other factors are fixed e.g. everything else is part of the $1,000 fixed cost package. (This would mean that raw material, transport, electricity etc would be fixed which would most certainly not be the case in a real firm!) Let me once again clarify that examples are often used to help you to understand concepts rather than depict reality. Total fixed costs are $1,000 per week and labourers have a wage of $500 per unit and week while quantity is at the same output rate as in the previous example. Putting these values into the table gives us the firm s total cost picture. Figure: 2.3.7 Q of labour (Q L ) Total output (Q) Total Fixed Costs (TFC) Total Variable Costs (TVC) Total Costs (TC) (= TFC + TVC) 0 0 $1,000 $0 $1000 1 40 1,000 500 1,500 2 90 1,000 1,000 2,000 3 130 1,000 1,500 2,500 4 140 1,000 2,000 3,000 5 130 1,000 2,500 3,500 Guess what we do now? Yes. Another diagram. This time, however, the object is to show costs, not output. The Y-axis becomes the cost axis while the X-axis is the output axis.
3/11 Fig. 2.3.8 Total cost picture at Sturdy-Pants 4,000 Costs ($) TFC are constant, while TVC and TC rise. The distance between the Q-axis and TFC is of course the same distance between TVC and TC. This is shown by the red double-sided arrows. 3,000 TC (TFC + TVC) 2,000 TVC 1,000 TFC 0 40 90 130 140 Q/week Total fixed costs: at an output of zero the firms still incurs costs of $1,000. This would be such factor costs as rent, depreciation of capital, insurance and administration personnel any costs which remain even thought the firm is not producing anything. Total variable costs: as output increases, so does the use of variable factors such as labour (which can also be fixed), raw material, electricity, water, components etc. (Note that variable costs rise faster after an output of 90 units of pants per week this is due to diminishing returns. See below.) Total costs: as no surprise, total costs are simply the sum of total fixed costs and total variable costs at a quantity of zero total costs are $1,000 (e.g. zero variable costs and only fixed costs) and at 140 units of pants total costs are $3,000 ($1,000 in fixed costs plus $2,000 in variable costs). Unit cost picture in short run (average and marginal costs) The total cost curve is just a way of showing the cost of total output at different quantities of pants per week in figure 2.3.8 above. Notice that total variable costs (TVC) and thus total costs (TC) increase at an ever slower rate at first but then at an increasing rate. This is in complete correspondence with the law of diminishing returns. We have put a price tag on the use of each unit of labour, and as the marginal output per given unit of labour starts to fall ultimately, then of course the cost of the additional output has to increase. Think of it this way: If labourer number 2 is getting $500 and adds 50 pairs of pants to total output, then the marginal cost of each of those pants is $500 50; $10 per pair. The next labourer adds 40 but gets the same wage increasing the marginal cost to $500 40;
4/11 $12.5. Once again, diminishing returns is another way of saying increasing marginal costs. The above is easier to see in a unit-cost picture. Moving from the total cost picture to the unit cost picture is no more of an intellectual jump than moving from total milk consumption in a household to the average quantity per person in the household and how much milk consumption changes when a friend stays overnight. Here are the formulae to help you make the jump: TFC. +. TVC =.. TC TFC / Q = AFC TVC / Q = AVC TC / Q = ATC In moving to the unit-cost picture, we divide the totals to arrive at averages. Marginal values are calculated TC MC = ----------- as Q. Fig. 2.3.9 Total and unit costs for Sturdy-Pants Total output (Q) TFC TVC TC AFC (TFC/Q) AVC (TVC/Q) ATC (TC/Q) 0 $1,000 $0 $1000 - - - 40 1,000 500 1,500 $25 $12.5 $37.5 90 1,000 1,000 2,000 11.1 11.1 22.2 130 1,000 1,500 2,500 7.7 11.5 19.2 140 1,000 2,000 3,000 7.1 14.3 21.4 MC ( TC / Q) 12.5 10 12.5 50 The table above is relatively uncomplicated, yet one point is worthy of comment. That is that it would be most difficult indeed to calculate MC as the cost of the last unit produced, which is why calculations are most often based on an average of the last batch, say the final 10 units produced in our example. The first 40 units have in fact an average marginal cost of $500/40 = $12.5 e.g. TC / Q. All the marginal cost values have been calculated like this. Putting the figures from figure 2.3.9 into diagrammatic form:
5/11 Fig. 2.3.10 The unit cost picture at Sturdy-Pants Costs ($) 50 MC 40 30 ATC min 20 10 0 ATC AVC AFC AVC min 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Q/t (pants/week) The distance from the Q-axis to AFC is the same as from AVC to ATC. Note the connection between the MC curve and both the AVC and ATC curves; the MC curve intersects both the average curves lowest points, i.e. AVC min and ATC min. We will return to this later as it is an important point in our definition of efficiency. Let us now briefly look at each cost curve in figure 2.3.10: Average fixed costs: I often compare TFC with spreading butter on a piece of bread; the more bread you spread a given amount of butter across, the thinner the layer. AFC falls continuously as we are spreading the fixed factor cost of $1,000 across increasing output. At an output of 40 units the AFC is $25 at output of 140 units, ATC is $7.10. Average variable costs: The AVC curve falls and then rises as diminishing average returns set in; unit costs rise because increasing the use of variable factors while fixed factors remain constant decreases the rate at which output increases. Average costs rise. Average total costs: Adding AFC to AVC we get the ATC curve, which also clearly portrays diminishing returns. Marginal costs: (MC) fall until around 70 units of output and then rise diminishing marginal returns set in. Linking total product to the unit cost picture diminishing returns revisited We are now back where we started; with diagrams showing how diminishing returns will arise in the short
6/11 run. The comparison below illustrates how falling marginal output is the same as rising marginal costs by comparing average and marginal product curves with ditto cost curves. Fig. 2.3.11 Comparing product curves to cost curves AP and MP Increasing marginal returns Diminishing marginal returns MP intersects with AP max AC and MC AP MP MC Q L The marginal and average variable cost curves are the other side of the coin, i.e. an inverted version of the marginal and average product curves. In attributing costs to the operation of the firm, the increase and decrease in the rate of production is shown by the U- shaped AC and MC curves. AVC MC intersects with AVC min Increasing marginal returns Diminishing marginal returns Q/t Falling marginal and average output rates and the U-shaped cost curves tell us that diminishing returns are present. Once again; diminishing returns are only possible in the short run and the short run is defined by the time period during which one or more factors of production are fixed. In the next chapter, we un-fix them.eh, we move into the long run where all factors are variable. Before we get to that, it is necessary to elaborate on the difference between a change in fixed costs and a change in variable costs. A change in fixed costs in the short run Assume that total fixed costs are at first $300,000 and double to 600,000. This means that the average fixed cost per unit goes from $30 at an output of 10,000 units to an AFC of $60. Of course this means that the AFC at 30,000 units goes from $10 to $20.
7/11 Fig. 2.3.12 An increase in fixed costs the roll of the ATC curve Costs 60 AFC will rise more (in absolute terms) at lower levels of output. This rolls the ATC curve upwards as ATC min will always intersect with the MC curve. Costs MC ATC 1 ATC 0 30 20 10 AFC 1 AFC 0 ATC min 10 30 10 30 Q/t (1,000s/month) Q/t (1,000s/month) Figure 2.3.12 shows that ATC rolls up the MC curve the increase in fixed costs causes the AFC curve to shift considerably more at low levels of output than at high ones. An increase in fixed costs say increased rent causes the AFC curve to shift upwards. The shift is uneven as fixed costs per unit at low levels will change far more than fixed costs at high levels of output. Therefore, in order for ATC to always intersect with the MC curve when AC is at the lowest point, the ATC curve will roll up the MC curve as shown in the diagram on the left. This is something many students find confusing when confronted with for the first time; why MC is unaffected by an increase in fixed costs. The reason is that marginal costs measure the change in total costs when an additional unit is produced. The rate of increase remains the same when total costs change by the same amount at all levels. A simple example is given in the table below, where fixed costs double from $100 to $200. This increases total costs at every output level by $100 yet the rate of change the marginal cost of producing an additional unit remains the same. 1 1 Favourite in-class trick: Take three students ranging from small to large, line them up in front of the class and put their heights on the board, e.g. 156 cm 166 cm 180 cm. What s the marginal rate of increase in height? It is 10 cm and 14 cm. Now guys, stand on your toes and now stand on a chair did the marginal values change? Would they change if you were on Mt Everest? It drives home the point that marginal costs do not change due to a change in fixed costs (disregarding the long run).
8/11 Total output (Q) TC 0 (FC = $100) 0 $100 1 110 2 118 3 127 4 139 MC 0 ( TC / Q) 10 8 9 12 Total TC 1 output (FC = (Q) $200) 0 $200 1 210 2 218 3 227 4 239 MC 0 ( TC / Q) 10 8 9 12 (Marcia: this might need some neatening up.cheers.) (Type 3 Medium heading) A change in variable costs in the short run A change in variable costs has the effect of shifting the MC curve. If the cost of, say, raw material falls then the cost of producing each additional unit will fall. The result is that the MC curve will shift downwards as in figure 2.3.13 below. At every output level the cost of producing an additional unit decreases, shifting the MC curve from MC 0 to MC 1. (Note that in keeping with the axiom that AC min will always intersect with the MC curve, the AC curve will also shift downwards.) Fig. 2.3.13 A decrease in variable costs Costs MC 0 MC 1 AC 0 AC 1 Q/t Lower costs of variable inputs (raw material for example) lowers the cost of each additional unit produced the MC curve shifts down from MC 0 to MC 1. QUESTION: What else could cause the MC curve to shift, other than a change in the cost of variable factor inputs? To summarise, a change in fixed costs will roll the AC curve up or down along the MC curve always keeping the AC min point at MC while a change in variable costs will shift the MC curve (and ATC curve). It is worth repeating that we have only dealt with the short run, i.e. one or more factors are fixed.
9/11 POP QUIZ 2.3.2: SHORT RUN AND THE FIRM 1. Assuming a firm where one or more factors of production are fixed and labour is the only variable factor, explain why total product (TP) will ultimately increase at a slower rate. 2. Continuing on question 1 above; what is the connection between TP and MP max? Use diagrams in your explanation. 3. Fill in the blanks: When MP turns negative, TP will. 4. Why do marginal and average costs ultimately rise? Would this be equally certain in both the long run and short run? Q 5. scrapped. 6. In increasing output from 5,000 units to 5,500 units, TC goes from 100,000 to 130,000. What is the MC per unit of the additional 500 units? 7. Why does a falling marginal product curve show the same thing as a rising marginal cost curve? 8. A rise in FC results in a disproportional increase in ATC! Explain. 9. Explain the effect on MC and AC when FC is tripled. Illustrate with a diagram. 10. Assume that the cost of variable inputs rises for a firm. How will this affect the unit-cost picture of the firm?
10/11 Calculating costs HL students will be required to calculate costs and illustrate them in diagrams in paper 3. Just bear in mind the following three points: 1) TC = TFC + TVC 2) ATC = AFC + AVC 3) MC = TC / Q Table XX Total output (Q) TFC TVC TC AFC AVC ATC MC 0 x 0 x x x x 10 x 35 x x x x 20 x 55 x x x x 30 x x x x 2.667* x 40 x x x x 3 x 50 x x 200 x 3.8 x (*Note; this value is rounded from 2 and 2/3.) Table XX above shows the total and unit cost picture for a firm. Fill in the missing values (x) and then a) Draw a total and unit cost picture. b) Explain why average and marginal costs at first fall and then rise. c) How would marginal costs be affected if average costs doubles? x x x x x
11/11 Summary and revision (need a cool pic here.maybe a pic of someone doing push-ups!) 1. Assuming one or more fixed factors gives the short run time span, e.g. there are fixed costs. This means that diminishing returns will ultimately set in. 2. The total cost picture shows total variable costs, tot fixed costs and total costs of production; TVC + TFC = TC. 3. The unit cost picture shows average and marginal costs of production average variable costs, average fixed costs and average total costs. AVC + AFC = ATC. 4. Marginal cost (unit cost picture) is the change in total costs over the change in output. Formulaically; MC = TC / Q. This is frequently put as...the cost of the last unit produced.... 5. The marginal cost curve will always intercept the AVC and ATC curves at their lowest points. 6. Marginal costs do not change when fixed costs change only average total costs are affected.