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Material for Week 2:
Optimization Techniques
Problem 3:
100
100
+
800
Interest rate (i) = 15%
100
900
PV 


767
.
49
1
2
(1.15) (1.15)
Problem 12:
Current Job = $30,000
New Job = $40,000
Return From Pharmacy = $200,000
Explicit Cost = 80,000+40,000+10,000+5,000 +8,000
= 143,000
Business Profit = 200,000 – 143,000 = 57,000
Implicit Cost = 40,000 + 2,000 = 42,000
Economic Profit = Business Profit – Implicit cost
= 57,000 – 42,000 = 15,000
(b) Total Revenue now is $200,000 which
includes a $15,000 economic profit. So in
three years when the new pharmacy will drive
down the economic profit to zero, total
revenue of the pharmacy will be $200,000 $15,000 = $185,000.
c. Samantha shall purchase the pharmacy if
the present value of the pharmacy is positive.
15,000
15,000
15,000
– 50,000
15,000
15,000
15,000
50,000
PV 



 1372. 57
1
2
3
3
(1  .15) (1  .15) (1  .15) (1  .15)
Demand Curve:
It shows the relationship between the quantity
demanded of a commodity with variations in
its own price while everything else is
considered constant.
Demand Curve:
Qd = 20 - .5P
P
P = 40 - 2Qd
40

0
Q
Supply Curve:
Shows the relationship between the quantity
supplied of a commodity with variations in its
own price while everything else is considered
to be constant.
Qs= – .15 + .3P
P
P = .5 + (10/3) Qs

0
Q
P
Excess Supply
25
0
7
Q
Profit = TR - TC
TR = P × Q
Q = 10 – .10P
P = 100 – 10Q
TR = (100 – 10Q)×Q = 100Q – 10Q2
AR = TR/Q = 100 - 10Q
when, Q  0
dTR d (100Q  10Q 2 )
MR 

 100  20Q
dQ
dQ
TR = 100Q – 10Q2
Q
TR
AR
MR
0
0
__
__
1
90
90
90
2
160
80
70
3
210
70
50
4
240
60
30
5
250
50
10
6
240
40
-10
TR
Q1 Q2
Q
Q3 Q4 Q5 Q6
MR
AR
AR
MR
Q
TC
TC
0
Q1
AC,
Q2
MC
Q
AC
MC
0
Q
Profit Maximization:
TC
TR
MC
p
Q1
Q2
MR
Q
Q
Optimization & Marginal Analysis :
Marginal Cost is defined as the change in total cost per
unit change in output and is given by the slope of the TC
curve. As long as the slope of the TR curve or MR
exceeds the slope of the TC curve or MC, it pays for the
firm to expand output and sales. The firm would be
adding more to its total revenue than to its total costs and
so its total profit would increase. To make it general,
according to the marginal analysis as long as the
marginal benefit of an activity (such as expanding output
or sales) exceeds the marginal cost, it pays for the
organization (firm) to increase the activity (expand
output). The total net benefit (profit) is maximized when
the marginal benefit equals marginal cost.