Bahan Mata Kuliah Matematika Ekonomi Gratis Terbaru - Kosngosan Situs Anak Kost Mahasiswa Pelajar Course 4
EQUATION IN ECONOMICS
(Course 4)
SYAIFUL HADI
DJAIMI BAKCE
NOVIA DEWI
JURUSAN AGRIBISNIS
FAKULTAS PERTANIAN
UNIVERSITAS RIAU
EFFECT OF A PER UNIT TAX
The information contained in the supply equation about
how much producers will supply is based on the prices that
they receive.
If a per unit tax (t) is imposed, although buyers still pay P
for each unit of the good, the suppliers receive only P – t.
The difference between the price paid and the price
received is the per unit tax (t), which is paid to the
government.
A per unit tax therefore change the supply equation and
causes the supply curve to shift.
Whatever the form in which the supply equation is written,
we can alter it to incorporate a per unit tax by writing P – t
in place of P wherever it occurs.
For example, if when there is no tax the supply equation is given
by
Q = -3 + 4P
then when a per unit tax of t is imposed the supply equation
becomes
Q = -3 + 4(P – t)
We rewrite them expressing P as a function of Q. The original
supply
equation becomes:
P = Q/4 + ¾
Writing P – t for P in the equation, the post tax equation is
P – t = Q/4 + ¾
Adding t to both sides this becomes:
P = Q/4 + 3/4 + t
The post tax values for P are t more than the original one, so when
we plot the two supply equation with P on the vertical axis the
post tax curve is higher by the amount of the tax.
If demand and supply in a market are described by the equation below, solve
algebraically to find equilibrium P and Q.
Demand : Q = 120 – 8P
Supply : Q = -6 + 4P
If now a per unit tax 4.5 impose, show the equilibrium solution changes. How is
the tax shared between producers and consumers ? Sketch a graph showing
what changes ensue when the tax is imposed ?
In equilibrium Supply Q = Demand Q
So equating the right-hand sides of the equation gives:
-6 + 4P = 120 – 8P
Adding 8P + 6 to each side we have:
12P = 126
Dividing by 12 gives: P = 10.5
Substituting in the supply equation gives:
Q = -6 + 4(10.5) = 36
The equilibrium values are P = 10.5 and Q = 36
When a tax of 4.5 is imposed the supply curve becomes:
Supply: Q = -6 + 4(P – 4.5) = -24 + 4P
In equilibrium this new quantity supplied equal the quantity demanded, giving:
-24 + 4P = 120 – 8P
Adding 8P + 24 to each sides gives: 12P = 144
and so dividing by 12 we find : P = 144/12 = 12
From the new supply equation we obtain: Q = -24 + (4 x 12) = 24
The equilibrium values are P= 12 and Q= 24. Although the tax is 4.5, price
has risen by only 12 – 10.5 = 1.5.
On third of the tax has been passed on to consumers as a price increase,
but
the remainder has been absorbed by the producers.
The quantity traded has fallen from 36 to 24.
To plot the curves we write the inverse function expressing P in term of Q.
We find:
Demand, D: P = 15 – Q/8
Original Supply, S : P = 3/2 + Q/4
Supply after tax, S : P = 3/2 + Q/4 + 4.5 = 6 + Q/4
Price changes = 1.5
S2 P= 6 + Q/4
S1 P= 3/2 +
Q/4
D P= 15 – Q/8
COST – VOLUME – PROFIT ANALYSIS
Cost – volume – profit analysis is a method use by accountants
to estimate the desired sales level in order to achieve a target
level of profit.
Two simplifying assumptions are made: namely that price and
average variable cost are both fixed.
= TR – TC ,
TR = P . Q
TC = FC + VC
AVC = VC/Q
Substituting in the profit function for TR and TC
= P . Q - (FC + VC) = P . Q – FC – VC
Multiplying both sides of the expression for AVC by Q we obtain
AVC . Q = VC
So we may substitute for VC in the profit equation and get
= P. Q – FC – AVC . Q
Adding FC to both sides gives:
+ FC = P . Q - AVC . Q
Interchanging the sides we obtain: P . Q – AVC . Q = + FC
Q is a factor of both term on the left so we may write:
Q(P – AVC) = + FC
Q = ( + FC) / (P – AVC)
If the firm accountant can estimate FC, P and AVC, substituting
these together with the target level of profit (), gives the
desired sales level.
For a firm with fixed cost of 555, average variable cost of 12
and selling at a price of 17, find an expression for profit in
terms of its level of sales, Q. What value should Q be to achieve
the profit target of 195 ? At what sales level does this firm
break even ? Illustrate your algebraic analysis with diagram.
= TR – TC = P . Q – FC – VC
writing VC = AVC . Q gives: = P . Q – FC – AVC . Q
Substituting cost and price we find: = 17Q – 555 – 12Q
So
= 5Q – 555
Which is the required expression for profit. Rewriting this to
give Q in term of add 555 to both sides so:
+ 555 = 5Q,
interchanging the sides gives: 5Q = + 555
and dividing by 5 we have :
Q = ( + 555) / 5
Substituting the profit target of 195 gives:
Q = (195 + 555)/5 = 150
For the break even value of Q we substitute instead = 0, so
Q = (555/5) = 111
LINIER EQUATION
y = 9x
Y=
18
As x increases, y does
not change
As x increases,
y increases
Slope = 0
Slope = 9
Line passes
through the
origin
A horizontal line has zero slope
Positive slope, intercept at zero
Slope = y/x = (distance up)/(distance to right)
Target Profit
Break even where TR =
TC
Cost – Volume – Profit Analysis
Larges x value go with
smaller y value
As x increases,
y increases
Slope= 3
Slope= -4
Y=504x
Negative slope, positive intercept
Line cuts y axis below the
origin
Positive slope, negative intercept
60
50
Y increases but x does not
change
Y
40
30
Slope=
20
10
0
0
5
10
X
15
A vertical line has infinite slope
20
JAWABAN PR/QUIZ
Rewriting these equations expressing P as a function of Q
then plot them on a graph
Supply : Q = 4P
Demand : Q = 280 – 10P
Supply: Q = 4P P = Q/4
Demand : Q = 280 – 10P 10P = 280 – Q
P = 28 – (Q/10)
Supply
Demand
(Course 4)
SYAIFUL HADI
DJAIMI BAKCE
NOVIA DEWI
JURUSAN AGRIBISNIS
FAKULTAS PERTANIAN
UNIVERSITAS RIAU
EFFECT OF A PER UNIT TAX
The information contained in the supply equation about
how much producers will supply is based on the prices that
they receive.
If a per unit tax (t) is imposed, although buyers still pay P
for each unit of the good, the suppliers receive only P – t.
The difference between the price paid and the price
received is the per unit tax (t), which is paid to the
government.
A per unit tax therefore change the supply equation and
causes the supply curve to shift.
Whatever the form in which the supply equation is written,
we can alter it to incorporate a per unit tax by writing P – t
in place of P wherever it occurs.
For example, if when there is no tax the supply equation is given
by
Q = -3 + 4P
then when a per unit tax of t is imposed the supply equation
becomes
Q = -3 + 4(P – t)
We rewrite them expressing P as a function of Q. The original
supply
equation becomes:
P = Q/4 + ¾
Writing P – t for P in the equation, the post tax equation is
P – t = Q/4 + ¾
Adding t to both sides this becomes:
P = Q/4 + 3/4 + t
The post tax values for P are t more than the original one, so when
we plot the two supply equation with P on the vertical axis the
post tax curve is higher by the amount of the tax.
If demand and supply in a market are described by the equation below, solve
algebraically to find equilibrium P and Q.
Demand : Q = 120 – 8P
Supply : Q = -6 + 4P
If now a per unit tax 4.5 impose, show the equilibrium solution changes. How is
the tax shared between producers and consumers ? Sketch a graph showing
what changes ensue when the tax is imposed ?
In equilibrium Supply Q = Demand Q
So equating the right-hand sides of the equation gives:
-6 + 4P = 120 – 8P
Adding 8P + 6 to each side we have:
12P = 126
Dividing by 12 gives: P = 10.5
Substituting in the supply equation gives:
Q = -6 + 4(10.5) = 36
The equilibrium values are P = 10.5 and Q = 36
When a tax of 4.5 is imposed the supply curve becomes:
Supply: Q = -6 + 4(P – 4.5) = -24 + 4P
In equilibrium this new quantity supplied equal the quantity demanded, giving:
-24 + 4P = 120 – 8P
Adding 8P + 24 to each sides gives: 12P = 144
and so dividing by 12 we find : P = 144/12 = 12
From the new supply equation we obtain: Q = -24 + (4 x 12) = 24
The equilibrium values are P= 12 and Q= 24. Although the tax is 4.5, price
has risen by only 12 – 10.5 = 1.5.
On third of the tax has been passed on to consumers as a price increase,
but
the remainder has been absorbed by the producers.
The quantity traded has fallen from 36 to 24.
To plot the curves we write the inverse function expressing P in term of Q.
We find:
Demand, D: P = 15 – Q/8
Original Supply, S : P = 3/2 + Q/4
Supply after tax, S : P = 3/2 + Q/4 + 4.5 = 6 + Q/4
Price changes = 1.5
S2 P= 6 + Q/4
S1 P= 3/2 +
Q/4
D P= 15 – Q/8
COST – VOLUME – PROFIT ANALYSIS
Cost – volume – profit analysis is a method use by accountants
to estimate the desired sales level in order to achieve a target
level of profit.
Two simplifying assumptions are made: namely that price and
average variable cost are both fixed.
= TR – TC ,
TR = P . Q
TC = FC + VC
AVC = VC/Q
Substituting in the profit function for TR and TC
= P . Q - (FC + VC) = P . Q – FC – VC
Multiplying both sides of the expression for AVC by Q we obtain
AVC . Q = VC
So we may substitute for VC in the profit equation and get
= P. Q – FC – AVC . Q
Adding FC to both sides gives:
+ FC = P . Q - AVC . Q
Interchanging the sides we obtain: P . Q – AVC . Q = + FC
Q is a factor of both term on the left so we may write:
Q(P – AVC) = + FC
Q = ( + FC) / (P – AVC)
If the firm accountant can estimate FC, P and AVC, substituting
these together with the target level of profit (), gives the
desired sales level.
For a firm with fixed cost of 555, average variable cost of 12
and selling at a price of 17, find an expression for profit in
terms of its level of sales, Q. What value should Q be to achieve
the profit target of 195 ? At what sales level does this firm
break even ? Illustrate your algebraic analysis with diagram.
= TR – TC = P . Q – FC – VC
writing VC = AVC . Q gives: = P . Q – FC – AVC . Q
Substituting cost and price we find: = 17Q – 555 – 12Q
So
= 5Q – 555
Which is the required expression for profit. Rewriting this to
give Q in term of add 555 to both sides so:
+ 555 = 5Q,
interchanging the sides gives: 5Q = + 555
and dividing by 5 we have :
Q = ( + 555) / 5
Substituting the profit target of 195 gives:
Q = (195 + 555)/5 = 150
For the break even value of Q we substitute instead = 0, so
Q = (555/5) = 111
LINIER EQUATION
y = 9x
Y=
18
As x increases, y does
not change
As x increases,
y increases
Slope = 0
Slope = 9
Line passes
through the
origin
A horizontal line has zero slope
Positive slope, intercept at zero
Slope = y/x = (distance up)/(distance to right)
Target Profit
Break even where TR =
TC
Cost – Volume – Profit Analysis
Larges x value go with
smaller y value
As x increases,
y increases
Slope= 3
Slope= -4
Y=504x
Negative slope, positive intercept
Line cuts y axis below the
origin
Positive slope, negative intercept
60
50
Y increases but x does not
change
Y
40
30
Slope=
20
10
0
0
5
10
X
15
A vertical line has infinite slope
20
JAWABAN PR/QUIZ
Rewriting these equations expressing P as a function of Q
then plot them on a graph
Supply : Q = 4P
Demand : Q = 280 – 10P
Supply: Q = 4P P = Q/4
Demand : Q = 280 – 10P 10P = 280 – Q
P = 28 – (Q/10)
Supply
Demand