II. Behavior of Firms Here, what we want to learn in the short-run analysis are as follows: (1) Average Total Cost (ATC), Average Variable Cost (AVC), and Marginal Cost (); (2) The contours of the curves that illustrate the concepts given in (1); (3) The shutdown point and the breakeven point; (4) That part of the marginal cost () curve that becomes the supply curve for the product; (5) Factors that shift the marginal cost curve, i.e., the supply curve. (1) ATC, AVC, and a. AVERAGE TOTAL COST (ATC): the total costs of production divided by the quantity produced (also called cost per unit) TC ATC,.. (1) Q Whether the ATC declines or increases depends on changes in TC (total costs) in response to changes in Q (or, the firm s output). Note that in order to increase Q in the short run we will change variable factors (or inputs) of production, e.g., workers, gasoline for trucks, fertilizer for crops and all other things. For simplicity, we consider L (laborer) as only the variable factor of production. Following this: as L (or labor) changes, Q and TC change. TC Q TC ATC Q Q TC = = = 1 ( ATC),.. (2) 2 2 2 Q Q Q Q Equation (2) shows: ATC ATC ATC > 0 if > ATC; = 0if = ATC; < 0if < ATC. ATC Note that since is the slope of average total cost curve, the slope is positive if ATC is greater than ATC. = 0 means the slope of the ATC curve is zero, when the ATC curve reaches its minimum point such as: 1
ATC ATC min b. AVERAGE VARIABLE COST (AVC): variable costs of production divided by the quantity produced. VC AVC Q VC VC Q VC AVC Q Q VC = = = 1 ( AVC),.. (3) 2 2 2 Q Q Q Q Now you see, the relationship between AVC and Q, i.e., equation (3), is the same as Equation (2). VC Why is =? Note TC = FC + VC, where FC is fixed no matter how Q changes. FC VC = + VC = 0 +, where... (4) Equation (4) shows that the marginal cost,, is obtained in two ways either by changes in TC due to a change in Q, or by changes in VC due to a change in Q. Then, when does the curve shift? Since we move along as Q increases. 2
Thus, Changes in Q will not shift the entire curve. 1 Thus, we need to find the factors that can shift the curve through any changes in variable costs. Now, for simplicity let VC=w L, where w is the wage rate per hour of labor and L is the quantity of labor hours. The variable costs, VC, change as either w or L changes. But, changes in L affect Q to change that will result in a movement along the curve. In our example only changes in the wage rate must shift the curve either upward (to the left) or downward (to the right). 2 (2) Shutdown and Breakeven points From Equations (2) and (3), the curve is smaller than the ATC and AVC curves, when the latter two curves, i.e., ATC and AVC, are declining. The curve is above the latter two curves when the two average cost curves are increasing. Finally, when ATC and AVC are at their minimums, =ATC and =AVC. These relationships can be shown as follows: ATC AVC, AVC ATC P P We name the point of intersection of with AVC, or =AVC as the shutdown point ( 操業停止点 ), and the point at which =ATC is called the breakeven point ( 損益分岐点 ). Shutdown point: the point at which price equals the minimum of average variable cost. That is, TR=VC and the entire loss is the amount of FC. Breakeven point: the point at which price equals the minimum of average total cost. That is, TR=TC=FC+VC. 1 As you may remember from the demand curve analysis, we move along the demand curve as the price of product changes. The entire curve of demand will shift as income, prices of other related products, tastes, and other factors which influence consumers, change. 2 Again, here I use only L as the variable factor in the production. In reality, variable factors ( 可変要素 )include not only workers, but also fuel, fertilizer, electricity and so on. 3
Therefore, when the price is lower than the minimum of average variable cost at the level of Q with P=, the TR does not cover all VC, i.e., covering only a part of VC, and no coverage for the FC at all. Thus, the firm had better not produce its output. (3) The Supply Curve by Firm P S the breakeven point the shutdown point The supply curve is the vertical segment on the P axis and the segment of curve at and above the shutdown point. (4) By the way, once more I would like to clarify the nature of the curve. Q TC FC VC 0 300 300 0 ---- 1 450 300 150 150 2 570 300 270 120 3 670 300 370 100 Do you notice any relationship between the VC and? Yes, if we add the values from the beginning, which equals the VC value. For example, the first VC and first are both 150. That is, both are equal. Now, if we add 150 and 120 of, which equals 270. Now, this 270 equals the value of VC (=270) at Q=2. The above statement can be shown in the following figure; the area under the curve is VC. 4
Where is the producer surplus? VC P E PS VC Producer Surplus: the difference between the price received by a firm for an additional item sold and the marginal cost of the item s production. Total Revenue = P x Q. The area is PEQ 0 0. VC: the area under the curve. Producer Surplus=TR-VC Note that the producer surplus is not profits, but profits + fixed costs. So, the Producer surplus is sometime called Rent. Rent: the revenues beyond the opportunity costs of input. Now, we define, as shown in figure, that the producer surplus is the area below the price but above the curve. P 5
P 0 Producer surplus Again, the producer surplus is the left-out portion of TR after the costs of variable factors is subtracted from the TR. (6) Now, I want to show when the curve shifts. In other words, what causes the supply curve to shift. Case I Case 2 (only VC changes) Q TC FC VC Q VC 0 300 300 0 ---- 0 0 --- 1 450 300 150 150 1 200 200 2 570 300 270 120 2 370 170 3 670 300 370 100 3 520 150 VC Since =, when the capital is fixed. That is, FC remains regardless of the level of Q. Thus, we should focus on factors which affect VC. Since VC is variable costs, i.e., expenditures on variable factors of production( 可変費用 ). Hence, if VC changes, must shift. In case 2, we increase the variable costs at each level of output in Case I by 50 per unit of output. So, we see the increases by 50 in Case 2. In this example, it is so obvious since we increase 50 per unit. Thus, the increases by 50 in case 2. Now, let us see in a different way to shift. VC FC since = if we use VC rather than TC since = 0, we will have: (by assuming that labor is only the variable factor in the production) VC = w L, where w is the wage rate (i.e., payments per hour of labor) and L is working hours. 6
Assume that the wage rate is given to the firm. So, VC changes as L changes. VC ( w L) w L w w = = = = =, MP L L where MP L is the marginal product of labor. IMPORTANT: In order to increase Q, we employ more L. But, due to the law of diminishing returns to labor (or the law of diminishing marginal productivity of labor), MP L increases but at a diminishing rate. This is why, we have an upward-sloping marginal cost curve or supply curve. So, as long as we change L (variable factors), we will not shift but move along the curve. BUT, if the wage rate rises, then the curve shift upward. w = 0 0 MP is given. Now, the wage rate increases from w 0 to w 1, we have: L w1 1 =. Then, since w 1 > w 2 then. MP, 1 > 2 L 1 when w=w 1 > w 0 0 when w=w 0 From the above example, I hope you see that the supply curve shifts upward (or to the left) or the supply of product decreases when prices of variable factors increases. On the contrary, if input prices fall, the curve shifts to the right or the supply curve increases. 7
(7) Finally, I would like to show how taxes affect the supply curve. Tax: an excise tax ( 物品税 )or sales tax A quantity tax ( 重量税 ) A value tax ( 従価税 ) Quantity tax: Tax per unit of physical output or weights. Value tax: Tax as a percentage of price such as our current consumption tax, 5%. Example 1: Now, let us assume that the government levies a 5-percent sales tax. We know we pay the tax. But we are not paying the tax directly to the government, but through firms. This sort of tax is called INDIRECT TAX (while income tax is DIRECT TAX). Now, we see how a typical firm behaves: Profits: Profits: π = TR TC, before the sales tax. π = (1 t) TR TC, after the sales tax, where t=0.05. The profit maximization after tax is: π = (1 t) The above result becomes: =. This is also, or (1 t ) MR = MR = or ( 1 t) ((1 t) TR) = 0. P =. Do you see what is going on here? ( 1 t) Since the firm accepts the price of product given in the market, P does not change to start with. But increases by 1/(1-t). That is, the supply curve decreases from s1 to s2 in I. Since the tax is not levied only on a firm but all firms in the industry, the supply curve in the market decreases from S1 to S2 in II. The price of product increases from P 1 to P 2. 8
I II S2 III (feedback) P s2 S1 s2 s1 P 2 P 2 P 0 P 0 D1 Note: q 2 < q 1 sales tax 0 q 1 q 0 q 2 q Firm A Industry Firm A after feedback Example 2: How about a quantity tax? Profits: π = TR TC, before the quantity tax, i.e., tax per unit of output. Profits after tax: π = TR TC tq, where t > 0 such as $2 per unit or 20 yen per unit. π = tq = t = 0 MR t = 0 MR = + t or P = + t Now, you can see the increase by the amount of t, i.e., quantity tax. P Supply after tax: +t Supply before tax: Amount of tax = t. 0 q 9
Example 3: How about tax on profits of the firm? Profits: π = TR TC, before tax on profits. Profits: ( 1 t) π = (1 t)( TR TC), after tax. π ( 1 t) = (1 t)[ ] = (1 t)( MR ) = (1 t)( P ) = 0 Since we can divide both the right and left of equation by (1-t). Nothing will change in the profit equation with and without the profit tax. Thus, there will be no changes in the firm s production. IMPORTANT: Any taxes or government policies that influence the firm s variable costs or productivity will affect the supply curve of its product. WHY? Example 4: Now, how about a fixed amount of tax (lump-sum tax: 一括税 ), T, regardless of the level of firm s production? Profits after tax: π = TR TC T, where T>0 is a given amount of tax or is fixed. π T Now, you see: = = 0. Thus, MR=, P=. Nothing will change the firm s behavior and, hence, no changes in its. 10