2. Definition
The power of the variable in the function is not 1
(it can be more or less than 1)
There are 4 types of non-linear functions that
used to be discussed in the economic analysis.
Those are:
a. Quadratic Function
b. Cubic Function
c. Exponential Function
d. Logarithmic Function
Find by your self the explanation of it. Give
example for each function (do it as homework)
3. Economics Application
1. Demand, Supply and Market Equilibrium.
The analysis is almost the same with the
analysis in the linear function
Market equilibrium still shown by Qd = Qs
The influence of Tax and Subsidy (changing
the selling price offered by the producer)
Supply func.change market equilibrium
change.
Tax leads to the increasing of equilibrium
price & the decreasing of equilibrium quantity
Subsidy leads to the decreasing of eq. price
& the increasing of eq. quantity
4. Example
a. Suppose Demand & Supply function of a product:
Qd = 19 – P2
Qs = -8 + 2P2
Determine the Equilibrium P and Q.
A we r:
ns
Qd = Qs
19 – P2 = -8 + 2P2
27 = 3P2
P2 = 9 P = 3
Q = 19 – P2 = 19 – (32) = 10
P = 3 ; Q = 10
5. Example
b. If for that product, specific tax is imposed at
the amount of Rp. 1/unit, then:
A we r.
ns
Q’s = -8 + 2(P-1)2
= -8 + 2(P2-2P+1)
= -8 + 2P2 – 4P + 2
= -6 + 2P2 – 4P
The new market equilibrium:
Qd = Q’s
6. Example
19 – P2 = -6 – 4P + 2P2
3P2 – 4P – 25 = 0
Using A formula, we find: P1 = 3,63 and
BC
P2 = -2,30 (irrational)
AB F ula:
C orm
P1,2 = (-b +/ √b2 – 4ac)/
- 2a
P = 3,63 Q’s = 5,82
In the imposition of TAX: P’e = 3,63 & Q’e =
5,82
7. Example
The tax that must be afforded by consumer
per product unit:
Tc = P’e – Pe = 3,63 – 3 = Rp. 0,63
The tax that must be afforded by producer per
product unit:
Tp = t – tk = 1 – 0,63 = Rp. 0,37
The tax that is received by the government:
T = Q’e x t = 5,82 x 1 = Rp. 5,82
8. Example
2. If we know that:
Qd = 40 – P2
Qs = -60 + 3P2
Calculate the equilibrium P & Q.
If to that product, government imposes tax at the
amount of Rp.2/unit:
a. Find the new equilibrium P & Q
b. How much the portion of tax that afforded by
consumer & producer?
c. How much the total tax that received by
government?
9. Example
a. Qs = -60 + 3P2
3P2 = Qs + 60
P = (√1/3Qs + 20)
After t = 2;
P = (√1/3Qs + 20) + 2
P – 2 = (√1/3Qs + 20)
(P – 2)2 = 1/3Qs + 20
P2 – 4P + 4 = 1/3Qs + 20
1/3Qs = P2 – 4P - 16
Q’s = 3P2 – 12P - 48
11. Cost Function
There are some specific terms in Cost
function, i.e:
a. Fixed cost : FC = k (k: Constant)
b. Variable cost : VC = f(Q)
c. Total cost : TC = FC + VC = k + f(Q)
d. Avr. Fix. Cost : AFC = FC/Q
e. Avr. Var. Cost : AVC = VC/Q
f. Avr. Cost : AC = TC/Q = AFC + AVC
g. Marginal Cost: MC = ∆C/∆Q
12. Example
a. The Total Cost of a firm can be illustrated as:
TC = 2Q2 – 24Q + 102
- At how many production unit, the total cost
of that firm is stated as minimum?
- In that production unit, Calculate the
minimum TC
- Calculate also the FC, VC, AFC & AVC
- If there is an increasing in the production at
the amount of 1 unit, how much the marginal
cost?
13. Example
Using the formula of parabola extreme point, TC is
minimum when: Q = -b/2a = 24/4 = 6 units.
TC min = 2Q2 – 24Q + 102
= 2(6)2 – 24(6) + 102
= 30
When Q = 6 and TC = 2Q2 -24Q + 102, then:
FC = 102
VC = 2Q2 -24Q = 2(6)2 – 24(6) = -72
AC = TC/Q = 30/6 = 5
AFC = FC/Q = 102/6 =17
AVC = VC/Q = -72/6 = -12
14. Example
If Q increases by 1 unit, then Q = 7 and
TC = 2(7)2 – 24(7) + 102 = 32
MC = ∆C/∆Q = (32 – 30)/(7-6) = 2
So, in order to increase production from 6 to 7,
that firm needs the marginal cost of 2.
15. Example
b. The Total Cost of a firm can be illustrated as:
TC = 5Q2 – 1000Q + 85000
- How much the TC if firm produce 90 units of
outputs?
- At how many production unit, the total cost
of that firm is stated as minimum?
- In that production unit, Calculate the
minimum TC
- Calculate also the FC, VC, AFC & AVC
- How much the marginal cost?
