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36 zero. Total variable costs (TVC), on the other hand, are costs which rise as output rises. Raw materials, labor, and transportation costs are all examples; the greater the firms production, the greater will be these costs. Should the firm produce nothing at all, these costs will be zero. \ 11 the list of real world total triable costs (sometimes just aariable costs for short) can be almost endless, we will make a strong simplifying assumpuon. Henceforth, we will consider only one type of total fixed cost, namely the cost of capital equipment and only one t)pe of variable cost, the cost of hiring labor. This artificial assumpuon permits us to simplily the analysis while concentrating upon the essentials of the theor) of the firm. Moreover, the assumpuon makes a certain amount of real world sense. After all, the firm can often fire all its workers in an instant, but it could take years to find a buyer for a highly specialized factory. In the long run, on the other hand, all costs are variable by definidon. In this case the firm has enough dme not only to hire or fire all the labor it likes, but also to enter, close, or expand any business. Hence capital becomes a variable cost in the long run. We emphasize that the short run does not necessarily imply a brief calendar ume span, nor does the long run imply a long one. For example, if a firms longest contractual commitment is a ninetynine year nonassignable building lease, the short run would last as much as ninetynine years and its total fixed cost would include the building rent throughout this period. On the other hand, if the lease were assignable to a subtenant who could be found within two weeks, the short run would last only two weeks if the firm had no other contractual commitments. In brief, the short run lasts undl the firm has enough dme to rid itself of all obligauons. Depending upon circumstances the calendar dme required may be brief or protracted and may vary from one firm to another. SHORT RUN TOTAL COST AND TOTAL VARIABLE COST CURVES In the following pages we will explore the reladonship between total cost (TC), total variable cost (TVC), and the firms output (q) in the short run, in which production increases can be achieved only by hiring more workers. We start with the relationship between a firms output and its total cost (TC), given in Figure 1. Total cost represents the entire opportunity cost necessary to produce a given output. In the short run, total cost is the sum of total fixed and total variable cost (TC = TFC + TVC). Therefore if the firm produces nothing, its total variable cost (TVC) will be zero, but it sdll must pay its total fixed cost (TFC) Thus, in Figure I, TC = TFC when q = 0. Moreover, the verdcal distance between total cost (TC) and total variable cost (TVC) represents total fixed cost (TFC). This distance is constant because total fixed cost is indeed fixed. As Figure 1 indicates, total cost (TC) rises as output increases. Under our assumpuon, this increase is due endrely to the purchase of more of the variable factor, labor. Moreover, the total cost curve rises first at a decreasing rate, the dashed poruon, then at an increasing one, the dotted portion. The overall "lazy S" shape of these curves can be explained as follows. First of all, total cost must always increase with output. This is only common sense. After all, the more output we produce, the more inputs we must buy Therefore the slope of the total cost curve must be positive. Now consider a short run factory situation with machines already in place. Clearly, the first worker hired will have no opportunities for specialization; he must staff the endre place. However, as more work1 ers are hired, each can specialize more. As we saw in ; Section I, specialization raises overall productivity.] Therefore as gains from specialization mount, the rate! at which the total cost curve increases slows down. This] is the dashed portion of Figure I; throughout this porl tion total cost rises at a decreasingrate. Do not let yourself get confused by this jargon; all it means is thatj the total cost curve, while rising, is getting flatten Specialization is not the only force at work,! hoAvever. As we add workers in order to increase outl put, each additional worker receives a decreasing! amount of the fixed factor, capital, to work with so thaH the amount of capital per worker falls and the workery Fig. I Short Run Total Cost Curves
Fig. II Derivation of and AVC          TVC            q, = 5 "I 
eventually begin to crowd and interfere with each other. As such effects begin to overpower gains from further specialization, the total cost curve starts to sharply rise. At this point, diminishing retiuns are said to set in, causing the total cost curve to rise at an increasing rate, that is, become steeper. In Figure I, diminishing returns set in at output level qi, where the dashed pordon of the total cost curve meets the dotted portion. The output q] is sometimes called the point of diminishing returns; it is the output at which the slope (steepness) of the total cost curve reaches a minimum. Up to qi the slope is falling; after qj its rising. In the short run, we must always eventually reach a point of diminishing retums such as q] To see this, imagine there were no diminishing returns. Then theoretically if we added enough variable factors such as fertilizer, gardeners, seeds, etc. to a single flower pot, we could grow the entire worlds food supply. Figure I also displays the total variabk cost (TVC) curve. Since total variable cost differs from total cost by the constant total fixed cost, the total variable cost curve is simply a vertical displacement of the total cost curve by the amount of total fixed cost. For example, if total fixed cost is $100, the vertical difference between these two curves would always be SI 00 in Figure 1. Like the total cost curve, the total variable cost curve displays a lazy S shape. But unlike the total cost curve, the total variable cost curve passes through the origin, since no variable cost is incurred at zero output. Also notice that the slope of the total variable cost curve equals the slope of the total cost curve at every level of output. SHORT RUN AVERAGE TOTAL & AVERAGE VARIABLE COST CURVES It is often more useful to work with the cost per unit instead of the three tolal costs. Dividing each term in the equation TC = TVC + TFC by quantit) q, it follows that: The first expression (TC/q) is termed average total cost ( ). The second (TVC/q) is termed average variable cost (AVC). The last term, (TFC/q), is called average fixed cost (AFC). Rewriting the "equation above in terms of these average costs we have: = AVC + AFC Fig. Ill Fig. IV
Clearly, ilwe know the value of any two of these three terms, we know the value of the other. For example, if at some level of output = $8 and AFC = $2, then AVC: = $6. Each of these three averages can be derived geometrically from their total cost counterparts and plotted as separate curves. In Figure II for example, we ha\e plotted total cost and total variable cost. Consider the level of output qi and lets suppose that qi represents five units of output. Now consider the rays from the origin to the total cost and total variable cost curves above q] The height (rise) of these rays gives us total cost (TC) and total variable cost (TVC) at qi, while their horizontal distance (run) of qj from the origin is simply the output, 5. It follows that the slope of these two rays, the rise over the run, is TC/qi and TVC/q] or average total cost ( ) and average variable cosi (AVC) respectively. For example, at the output of 5 units, total cost (TC) is $20 and total variable cost (TVC) is $10 so that the slope of the rays, average total cost ( ) and average variable cost (AVC), are $4 per unit ($20/5) and $2 per unit ($10/5) respectively. If we repeat this procedure at every other level of output, we can generate the average total and average variable cost curves of Figure III. Sue poinU are thus derived in the figure. Note that average fixed cost (AFC) is the verdcal difference between average total cost ( ) and average variable cost (AVC) and is equal to $2 at qi ($4  $2). Average fixed cost (AFC=TFC/q) declines condnuously as the output q in the denominator rises. If on the other hand we begin with the three average curves, we can recover the corresponding total curves by recalling diat TC = (ATC)q, TVC = (AVC)q, and TFC = (AFC)q. For example, in Figure IV total cost at the output qj is the endre shaded area ($20 = $4 X 5), while total variable cost at qi is the dotted area ($10 = $2 X 5). Total fixed cost (TFC), (AFC)q, is die dashed area. SHORT RUN MARGINAL COST CURVES Next we look at the central concept of marginal cost (MC). Marginal cost is the change in total cost, , divided by a small (usally one unit) change in output, i.e., MC = ATC/Aq, where Aq, the change in ouput is one unit. Referring to Figure V and die definition, marginal cost at any particular output is (formally) the slope (steepness) of the tangent to the to total cost curve at that output. In other words, if the slope of the total cost curve at the output 5 units is $1 per unit of output, we would plot the MC at 5 units as $1 in Figure VI. In Figure V, tangents are drawn at le\ els of output qi = 5, qg, and qg, and the associated mar ginal cost is displayed in Figure VI. Since the slope of the total cost curve falls throughout the dotted portion of the curve and rises thereafter, it follows that mar ginal cost falls throughout the dotted portion and rises at higher levels of output. As an (informal) numerical example, if the total cost of producing 5 units is $10, and the total cost of producing 6 units is $13, the mar? ginal cost (MC) of die 6th unit is about $3 ($13  $10); $3 would also be the approximate slope of the tangeill to the total cost curve at 6 units. In working problems we typically use die informal definition. In Figure VII wc impose the marginal curves just derived onto the average total and varia cost curves from Figure III. Note that die niargi cost (MC) curve passes through the minimum of bo Fig. VI 4, =5
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