Và cũng vốn là khu vực duy nhất trong đó sản xuất sẽ diễn ra. Mức độ chính xác của lao động và sử dụng vốn trong giai đoạn II trong đó sản xuất sẽ xảy ra không có thể được xác định tại thời điểm này. Đối với một công ty tối đa hóa lợi nhuận, | Unconstrained Optimization The Profit Function 287 Equation expresses profit not directly as a function of output but as afunction of theinputs employed inthe production process in this case capital and labor. Equation allows US to examine the profit-maximizing conditions from the perspective of inpuI. usage rather than output ì eve I Si Taking Ịsatdo graivatsvcr on I .qeation rrczia wcth. respect te capital hod labor tTe tirst-order aonditvont for profit maximization are ei- ngdổt n n ta ttrg-o ii dK UK TL-41K Pl 722b The second-order condition for a profit nodmum is cm - . 0 - thini dU WgUviVCatviad Equations may be rewritten as po tMPx T P0xnt JOL SSs The term on the left-hand side of liquations is called the marginal revenue product of the input while the 4 oh t h right which is the rental price of the input is called the marginal reso urce cost of the input. Equations mnybaeoprnssedar MRPK so MRCK tZ PPh MRP Equations are easily interpreteS. 1 .qiialioi for example says that ạ hrrn will hire additional inceernsnthn eUs ot capital to the point at which the additional revenues brought Rto the firm are precisely equal to the cost ofatrieh an incrcmmiialuiiit. arcneitmLaincethe marfinal product s fh t l na labor IhII cgaitiennl -nitr o cxpi-alaaehtscd because ottOeOaw ol eimmirhmg mashina-prodgx- and Rea MPPx MRCk hicmo oac more unit o1 eapifat Rifi rcsi ii in -he firm losing money on the lastenitoh capital lured iHirinhonvilnieee2ighantheamaantor capital req cI red to sadfy Eqostioa maans that. the fiam ia ter going profit theteou d hnve hoen eaenndOy hSsingadditionniumt2oSnnpi al emce MRPk MRCKi ProMe nZ onluncnontacRgaliom is Q K5L5 288 Profit and Revenue Maximization The firm can sell all of its output for 4. The price of labor and capital are 5 and 10 respectively. a. Determine the optimal levels of capital and labor usage if the firm s operating budget is l ooo. b.
