Tough Decisions
The Economic Reasoning
Behind Firms Decisions
Our Experiment
Model Principles of:
– Production Function
– Supply Curve
– Average Total Cost Curve
Conditions
–
–
–
–
Wage = $5 per hour
Hour = 1 minute
Capital fixed at 3 staplers
Demand is constant
Regression
n 7
 yi   axi 2  bxi 



i 0
Least Squares Problem:
Optimization
–
y
0
a
2
y
0
b
Table 1: Production Function
Q
120
100
PF = Q(L) = -1.1464L2 + 21.412L
R2 = 0.997
80
60
40
Production
Production Function (PF)
20
L
0
0
1
2
3
4
5
6
7
8
9
10
Production
Production Function: Q(L)
– Regression
Q’(L) = MP(L)
Law of Diminishing
Return
Laborer gets hired when
P x Q’(L) = Wage
L
Q
P
W
MPL
VMPL
TR
∆Profit
0
0
$0.50
$5
-
-
-
-
1
17
$0.50
$5
17
$8.50
$8.50
$3.50
2
36
$0.50
$5
19
$9.50
$18.00
$4.50
3
54
$0.50
$5
18
$9.00
$27.00
$4.00
4
69
$0.50
$5
15
$7.50
$34.50
$2.50
5
80
$0.50
$5
11
$5.50
$40.00
$0.50
6
88
$0.50
$5
8
$4.00
$44.00
-$1.00
7
92
$0.50
$5
4
$2.00
$46.00
-$3.00
Regression Equation for Production
Function
n 7
f (a, b)   Qi  (aLi 2  bLi ) 
2
i 0
f
 22854  9352a  1568b  0
a
f
 4198  1568a  280b  0
b
4198  280b
a
1568
f
 4198  280b 
 22854  9352 
  1568b  0
a
1568


b  21.412
a  1.146
Q( L)  1.146 L  21.412 L
2
Integrals
Area under the curve:
costn
–

t
f '( x)dx  f (n)  f (t )
Area above the curve:
surplus
– Box minus cost
The Supply Curve
Constant Demand
Supply as a function
– MC(Q)
– As quantity rises, input
costs rise too
– Regression
Producer Surplus
– Benefit
– Equilibrium
– Integrals
Cost of Production
Producer Surplus using definite
integrals
MC (Q)  MB (Q )
Table 2: Competitive Market
P
$0.80
S = MC (Q) = 0.1595e0.0158Q
2
R = 0.6097
$0.70
0.1595e
0.0158Q
 0.5
2
ATC(Q) = 0.0001Q - 0.0132Q + 0.7766
R2 = 0.9829
$0.60
$0.50
$0.40
$0.30
Q  72
$0.20
$0.10
$0.00
0

72
0
0.1595e
0.0158Q
10
20
30
40
50
60
70
80
Demand
Supply
ATC
Demand Curve (D)
Supply Curve (S)
90 ATC Curve
100 Q
dQ  21.39392801
36  21.39392801  14.60607199
Cost and Profit
Average Total Cost
– Total Cost / Quantity
Variable Cost
Fixed Cost
– Curve Shape
2nd degree polynomial
Concave up
Profit
– Quantity multiplied by
the difference in price
and average total cost
Conclusions
The models were correct!!!!