EQUATION IN ECONOMICS
(Course 4)
JURUSAN AGRIBISNIS
FAKULTAS PERTANIAN
UNIVERSITAS RIAU
SYAIFUL HADI
DJAIMI BAKCE
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
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
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
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
S2 P= 6 + Q/4
S1 P= 3/2 +
Q/4
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
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
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
LINIER EQUATION
A horizontal line has zero slope
As x increases, y does not change
Slope = 0
Slope = y/x = (distance up)/(distance to right)
Y = 18
As x increases, y increases
y = 9x
Slope = 9
Line passes through the origin
Break even where TR = TC
Target Profit
Slope= -4
Larges x value go with smaller y value
Line cuts y axis below the origin
Negative slope, positive intercept Positive slope, negative intercept
0
Y increases but x does not change
Slope=
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
