Lecture # Costs of Production

Transcription

1 I. Which Csts Matter? Lecture # Csts f Prductin Having defined prductin, the next step in the firm's prblem is cst minimizatin. T begin, we discuss which csts ecnmists are cncerned with. Ecnmic csts vs. accunting csts Accunting csts fcus n explicit csts (e.g. wages, rent, cst f materials...) Ecnmic csts als include pprtunity csts. Opprtunity cst -- the cst f frgne pprtunities. Ecnmic csts ignre sunk csts. Sunk csts -- expenditures that have been made and cannt be recvered. Since sunk csts cannt be changed, they shuld nt influence the firm's decisin. II. Csts in the Shrt Run A. Definitins Ttal cst (TC) -- the ttal amunt a firm spends t prduce a given level f utput (Q). Can be divided int: Fixed cst (FC) -- a cst that des nt change as the quantity f utput changes. Variable cst (VC) -- a cst that des change as the level f utput changes. Marginal cst (MC) -- the increase in cst that results frm prducing ne extra unit f utput. Marginal cst is equal t changes in variable cst. Average cst (AC) -- the cst per unit f utput.

2 B. Cst Curves Key features f cst curves: AC & MC are U-shaped curves. Nte that they are related t the average prduct and marginal prduct curves. When MP f labr is rising, MC falls, and vice versa. When AP f labr is rising, average variable csts (AVC) fall, and vice versa. Nte that the relatinship between AP and AC is nt exact, because AC als includes fixed csts. MC intersects the average cst curves at the minimum f each average cst curve. Als, nte the inverse relatinship between marginal prduct and marginal cst: Increasing returns t labr => decreasing marginal csts. Decreasing returns t labr => increasing marginal csts. Shifting the curves Things that affect variable csts shift bth the AC and MC curves. Example: a tax n labr.

3 Things that affect fixed csts nly shift the AC curve. Example: increase rent n a factry III. Csts in the Lng Run A. Iscst Lines Iscst line -- a line representing all pssible cmbinatins f inputs that can be purchased fr a given ttal cst. slpe = -w/r Csts increase as the iscst line shifts ut. An iscst line is similar t the budget cnstraint frm cnsumer thery.

4 B. Minimizing Csts Gal: T find the cmbinatin f inputs that prduces a given level f quantity at the lwest pssible cst. Occurs where an iscst line is tangent t the isquant. Cnsider the three iscst lines belw. Our gal is t minimize the cst f prducing the quantity represented by the isquant. The purple line allws us t prduce the desired quantity. Hwever, we wuld spend t much. The blue line des nt spend enugh. It is nt pssible t prduce the desired quantity. The green line is the lwest pssible iscst line tuching the isquant. This is the cheapest way t prduce this utput. At this pint, MPL/MPK = w/r, r: MPL/w = MPK/r The marginal prduct per dllar spent n each input is equal! Intuitin: Each dllar f input added t prductin adds an equivalent amunt f utput. Suppse they are nt. Fr example, the marginal prduct per dllar f labr is tw, and the marginal prduct per dllar f capital is ne. If yu spend ne less dllar n capital, yu lse ne unit f utput. If that dllar is spent n labr, yu get tw additinal units f utput. Thus, there is a net gain f ne unit f utput fr the same cst as befre.

5 Nte: if the price f an input changes, the slpe f the iscst line changes. Hwever, cst minimizatin requires that we stay n the same isquant. As a result, the firm uses less f the input whse price has increased, and mre f the ther. In the example belw, the firm staarts with KA and LA. Csts are shwn by the blue iscst line. As the cst f labr increases, the iscst line becmes steeper (similar t when it rtated in when wrking with budget cnstraints). At this pint, the firm uses mre capital (KB) and less labr (LB). Nte as well that the intercept n the K axis is higher. Since the price f capital hasn't changed, this must mean that ttal csts are higher with the green iscst line.

6 IV. Ecnmies f Scale The lng run ttal cst curve fllws frm cst minimizatin. By varying the level f utput (that is, lking at different isquants), cst minimizatin tells us the cheapest pssible way t prduce any given level f utput. The shape f the lng run ttal cst curve is determined by ecnmies f scale. Recall that returns t scale kept inputs in the same prprtin (e.g. duble inputs => duble utput). Hwever, in the lng run, the prprtin f inputs can change. Thus, we lk at changes in cst. Ecnmies f scale -- when yu can duble utput fr less than duble the cst. Disecnmies f scale -- when yu duble utput and csts mre than duble. Ecnmies f scale help determine the shape f the lng run AC curve MC < AC (AC falling) => ecnmies f scale MC > AC (AC rising) => disecnmies f scale U-shaped AC curves are typical fr cmpetitive markets. In these industries, it makes since t have several small firms t avid disecnmies f scale. Mnplies are ften the result f ecnmies f scale. When average csts fall as utput increases, it makes since t have ne firm prduce the utput.