Production and Costs - Excel by maclaren1

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									EE 311 Microeconomics Theory: I. Total product and
                      30
                     Q
 Chayun Tantivasadakarn
 Thammasat University 25                                                         p*
                                                                                   TPL
Competitive Factor Market
                                         20                       B               p2
Wage (w) = 6.25      25              Q*
                                                                                  p1
                                         15
Price (P) = 2.6      13
Assumptions:                             10
  TPL = aL - 0.5bL
                          2
                    Therefore,          p*/P*
  MPL = a - bL and VMPL5 = (a-bL)P
A profit maximizing firm will choose to hire 0                                             L
  L* which causes VMPL = w as shown in                                 L* 5 6 7 8
                                                0    1    2    3    4
  Graph II. L* then generates Q* and 16
                                     Wage Rate


  profit p* as shown in Graph I. Notice14
  that it is the same Q* in Graph IV which  12
  causes MR = MC.
                                            10
The iso-profit line in Graph I is derived from
  p = PQ - wL assuming a constant profit, p, 8                          VMPL = w
                                            W                                         SL
                                             6
   which gives the equation Q = (p + wL)/P.
                                             4
Note that at point B the slope of TPL (or MPL)
  equates to the slope of the iso-profit line2 (w/p)                                 DL
  (or w/p) which implies that VMPL = w. 0                                                  L
                                                                      L*
Solutions:                                       0   1    2    3    4     5   6    7     8
       L* = 4.50 <-- from (a - bL)P = w                II. Firm's labor demand and
                                                        2
      Q* = 18.89 <-- substitutes L* in Q = aL - 0.5bL
      p* = 21.02 <-- substitue Q* in PQ* -wL*
Note: The area under the VMPL curve up to L* represents total revenue when the firm produces up to Q*. Theref
  As a result the maximum profit that generates by L* is the area trapped under the DL curve and above the SL c
                                                    III. 45O Line for turning the                  Production assumptions
                              Q 30                                                                   TPL = aL - 0.5bL
                                                                                                                      2

                p*                                                                                  MPL = a - bL
                 TPL            25
                                                                                    45O line       VMPL = (a - bL)P
                p2
                                20                                                                 where        a=        6
                               Q*
                p1                                                                                              b=      0.8
                                15                                                                    L      TPL MPL VMPL
                                                                                                   0.0001         0       6 16
                                10
                                                                                                      0.5      3      6    15
                                 5
                                                                                                        1      6      5    14
                          L               45o                                                         1.5      8      5    12
                                 0
                                                                       Q*                      Q
                                                                                                        2     10      4    11
                      8               0         5        10      15     20      25        30
                                 6                                                                    2.5     13      4    10
                                                                                                        3     14      4     9
                              Price




                                 5
                                                                              MC
                                                                                                      3.5     16      3     8
                                 4                                                                      4     18      3     7

                                 3                             MR = MC          D = MR                4.5     19      2     6
                 SL             P                                                                       5     20      2     5
                                 2                                                                    5.5     21      2     4
                                                                                                        6     22      1     3
                                 1
                DL                                                                                    6.5     22      1     2
                          L      0                                                             Q        7     22      0     1
                                                                       Q*
                      8               0         5         10     15      20     25        30          7.5     23      0     0
                                           IV. Firm's demand and supply for                             8     22      0    -1


nue when the firm produces up to Q*. Therefore, the profit must be equal to this area subtracts by the total cost which is wL*.
pped under the DL curve and above the SL curve or 0.5 x L* x (a - w).
                                         Coordinates for Q* on TP       45 Degree line
                                           L       TPL                     X      Y
                                              0 18.89                         0       0
                                           4.50 18.89                        28      28
                                           4.50 0.00
                                           4.50 18.89                   Switching line
                                           8.00 18.89                     X         Y
                                                                              0 18.89
                   Iso profit Lines I    Iso profit Line: Q* = (Pi*+w*L*)/P* 18.89 18.89
                      L     Q               L     Q                       18.89       0
                         0 0.00                0 8.08
                      4.50 10.81            4.50 18.89                  MR Line
                      7.00 16.83            7.00 24.91                  Q      P
                                                                             0   2.6
                   Iso profit Lines II   Facing supply of Labor             30   2.6
                      L         Q           L      w
                         0 4.04                0       6                MC Line
                      4.50 14.85            4.50       6                Q      MC L
                      7.00 20.87            8.00 6.25                      0.00 1.04         0.00
                                                                           9.65 1.38         1.83
                                         Coordinates for L*               14.39 1.73         3.00
                                           L        w                     18.89 2.60         4.50
                                           4.50       16                  21.27 4.46         5.75
                                           4.50        6                  22.40 15.63        7.00
                                           4.50        0
                                                                        Coordinates for Q*
ts by the total cost which is wL*.                                      Q       P
                                                                          18.89       6
                                                                          18.89     2.6
                                                                          18.89       0
                                                    Faculty of Economics, Thammasat University


             Competitive Factor Market and Output
             Market




Production and Costs:                          4                      Chayun Tantivasadakarn
                                                                                  Faculty of Economics, Thammasat University




                    Output per period                                    D
                                                                                              TPL(K)
                                                          C
                            Inflection point                                       (a) Total Product


                                                     B

                                         A
                        O
                    Output per period LA             LB       LC          LD                   Labor

                                               B/                                 (b) Average Product
                                   A/                         C/=C//
                                               B//
                                   A//                                       D/

                                                                                             APL(K)
                                                                          D/
                        O               LA           LB       LC        LD        MPL(K)        Labor
                                    Figure 2: Total, Average, and Marginal Product




Production and Costs:                                              5                                Chayun Tantivasadakarn
                                                            Faculty of Economics, Thammasat University




                ฿                                              TC
                                                        C
                        (a) Total Cost Curves
                                 A                              TVC
                                                    B


Production and Costs:                           6                             Chayun Tantivasadakarn
                                                                  Faculty of Economics, Thammasat University




                                                                                  TFC

                                                                                   Q
                                 Q1                         Q2 Q3
                 ฿
                                                                   (b) Average and marginal
                                                                     MC
                                                             C/           AC
                                                                               AVC
                                                       B/


                             A/                                             AFC
                                                                                   Q
                               Q1                        Q2 Q3
                        Figure 3: Relationship between cost curves




Production and Costs:                         7                                     Chayun Tantivasadakarn
                            Faculty of Economics, Thammasat University




Production and Costs:   8                     Chayun Tantivasadakarn
Questions:
1. From the total product, and the given output price, P, and the wage rate, w, sovle the funtional form
   for the optimum level of L* that maximize profit.
2. From the profit function, show that the iso-profit function is linear with a vertical intercept = p/P
   and a slope given by w/P.
            3

								
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