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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
