# Production and Costs - Excel by maclaren1

VIEWS: 32 PAGES: 9

• pg 1
```									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

```
To top