Economics 104 - Profit Maximization and Employment of Factors PDF

LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez ECONOMICS 104 Topic 2: Profit Maximization and Employment of Factors LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez LEARNING OBJECTIVES At the end of the topic, the learners should be able to: exp...

LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez ECONOMICS 104 Topic 2: Profit Maximization and Employment of Factors LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez LEARNING OBJECTIVES At the end of the topic, the learners should be able to: explain key concepts related to factor market analysis analyze the dual effect response of firms to change in factor prices demonstrate profit maximization under perfectly competitive product and factor markets 1 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez PROFIT MAXIMIZATION Recall: Profit Function Profit Function can also   TR(Q)  TC(Q) be written as: Profit max condition:   TR( K , L)  TC ( K , L) d dTR dTC  TR( K , L) TC ( K , L) 0  0 0  0 dQ dQ dQ K K K dTR dTC   TR( K , L) TC ( K , L) 0  0 dQ dQ L L L MRPK  MFCK MR  MC MRPL  MFCL LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Marginal Revenue Product additional revenue gained from the output produced by the additional input used TR(Q) TR(Q) Q MRPL    MR x MPL L Q L Marginal Factor Cost additional cost incurred by using an additional input TC ( K , L) TC ( K , L) MFCK   r; MFCL  w K L 2 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Marginal Value Product value of the additional output produced by the additional input used Q MVPL  P  P x MPL L Graphically, we can derive the optimal input: MVPL, MFCL, MRPL , MPL w MFCL MVPL= PxMPL MPL L* L LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Try this! An alternative way of deriving the optimization condition is using the Lagrange Multiplier Method Hint: (1) λ = MC (2) MR = MC or P=MR=MC (PCM) LE: Z  rK  wL    Q( K , L)  Q0  FOCs Use Hint (1) Use Hint (2) MRPK  MFCK ; MRPL  MFCL 3 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Single-Input Demand Case (PCM) What is the relationship between wage and the amount of labor employed by a firm? the cheaper the cost of hiring an input, the greater the amount of that input a firm can purchase, cet. par. Another way of looking at it: w  P MPL  w  P MPL   MPL  L  w  L LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Graphically: MVPL, MFCL w MFCL w’ MFCL’ MVPL= PxMPL L* L’ L L w and L are inversely related; 0 w 4 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Numerical Example: Q  100 L P  50 w  500   TR  P  Q  50 100 L  5,000 L TR  MVPL  2,500 L0.5 L w  MVPL 500  2,500L0.5 L0.5  5 L*  25 Q*  100 25  100(5)  500 Try this! try changing the value of w to verify the inverse relationship of L and w LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Two-Input Demand Case (PCM) Note: We CANNOT just do two separate single-input demand analysis for each input for the two-input demand case If the wage rate increases, there will be changes in both L and K as the new cost minimizing combination is chosen The effect on the inputs can be broken into two parts: Factor Substitution Effect (FSE) Output Effect (OE) 5  LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Factor Substitution Effect Consider an increase in the wage rate from w to w’ As w increases, w r also rises to say, w ' r L becomes relatively more expensive than before The original combination L0 , K 0  is no longer cost-minimizing, i.e. MRTSLK 0  w' r LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez The firm must shift to the relatively less expensive input, K w' Find 1 MRTS LK  K r w' 1 MRTS LK  slope   w' r r K’ B A w K0 0 MRTS LK  r L’ L0 L 6 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Conclusion (via FSE): L K 0 0 w w Recall: w MPL   MPL w   MRTS LK   MPK r  r MPK   MPL  L  MPK  K Homework: show FSE for a decrease in the wage (also, increase and decrease in rent) LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez BUT! the demand for factors does not depend only on cost minimization the firm’s main objective is to maximize profit the higher price of an input resulted to a change in the marginal cost structure of the firm and thus, affects the firm’s profit maximizing condition 7 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Output Effect Consider an increase in the wage rate from w to w’ increase in w will increase the cost of producing Q the MC of producing Q is now higher at w’ MC is now greater than MR (MC>MR) and thus it will be profit maximizing to decrease Q less Q requires less L and K LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Conclusion (via OE): dQ * dL * L 0 0 0 dw dQ * w dQ * dK * dK 0 0 0 dw dQ * dw 8 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Net Effect NE = FSE + OE Recall: FSE: dL 0 dK 0 dw FSE dw FSE dL dK OE: 0 0 dw OE dw OE dL dL dL dK dK dK   0 NE: dw NE dw FSE dw OE dw  dw  dw 0    NE FSE OE ( ) () () () LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Recall: Isocost Suppose the price of L (w) increases: K C/r C/w’ C/w L 9  LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Graphically: Case 1 K FSE B K1 A K0 = K2 OE C Q NE=0 Q’ L2 L1 L0 L OE FSE NE LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Graphically: Case 2 K FSE B K1 C K2 A OE K0 NE Q Q’ L2 L1 L0 L OE FSE NE 10  LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Graphically: Case 3 K FSE B K1 A K0 K2 NE OE C Q Q’ L2 L1 L0 L OE FSE NE LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Try this! Analyze the FSE, OE and NE for a wage decrease (also for an increase and decrease in rent) Numerical Example: Q  40K 0.25 L0.25 wr 4 P 1   P  Q  TC ( K , L)    40K 0.25 L0.25   4K  4L FOCs:   0  10 K 0.75 L0.25  4  0; 4  10 K 0.75 L0.25 K   0  10 K 0.25 L0.75  4  0; 4  10 K 0.25 L0.75 L 11 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Using the FOCs, we have: 4 10 K 0.25 L0.75  KL 4 10 K 0.75 L0.25 Substituting back to any of the FOCs: 4  10( L)0.75 L0.25 L0.5  2.5 L*  6.25 K *  6.25 To solve for Q*, substitute the computed L* and K * to the production function: Q*  40( K *)0.25 ( L*)0.25 Q*  100 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez Try this! Mathematically show the FSE and OE from the previous example. Hint: (1) Q  400P 2  rw 0.5 (2) For FSE, keep the value of Q equal to 100, then solve for L* and K* using cost minimization (3) For OE, find first the net/total effect (NE), then get the difference between the FSE and NE 12 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez LEARNING OBJECTIVES At the end of the topic, the learners should be able to: explain key concepts related to OR factor market analysis analyze the dual effect response of OR firms to change in factor prices demonstrate profit maximization under perfectly competitive OR product and factor markets LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez REFERENCES Nicholson, W. and Snyder, C. 2007. Microeconomic Theory: Basic Principles and Extensions. 10th Ed., South-Western, Cengage Learning, pp 374-378. Varian, H. 2010. Intermediate Microeconomics: A Modern Approach, 8th Ed. New York: WW Norton and Co. Note: Learning resources can be accessed in our ECON 104 eLBI Course Site at http://ilcecourses.uplb.edu.ph/course/ 13 LMAT-A2 Learning Facilitator: Paul Joseph B. Ramirez END OF TOPIC 2 Topic 2: Profit Maximization and Employment of Factors Next Topic: Marginal Productivity Theory of Demand and Factor Shares 14