EQUATION IN ECONOMICS
(Course 3)
JURUSAN AGRIBISNIS
FAKULTAS PERTANIAN
UNIVERSITAS RIAU
OLEHSYAIFUL HADI
INTRODUCTION
An equation is a statement that two expressions
are equal to one another.
In economic modelling we express relationships
are equations and then use them to obtain
analytical result. Solving the equations gives us
values for which the equations are true.
We can express the condition for market
REWRITING AND SOLVING
EQUATIONS
When rewriting equation:
1. Add to or subtract from both sides.
2. Multiply or divide through the whole or each side (but don’t divide by 0).
3. Square or take the square root of each side. 4. Use as many stages as you wish.
5. Take care to get all the signs correct.
Example: Plot the equations y = -5 + 2x and y = 30 - 3x. At what
values of x and y do they cross ? Find also the algebraic solution by setting the two expressions in x equal to one other.
We are asked to plot two linier functions, so plotting two points on each then connecting them will suffice.
y=-5+2x
y=-30-3x
x 0 2 4 6 8 10 12
y=-5+2x -5 -1 3 7 11 15 19
y=30-3x 30 24 18 12 6 0 -6
For algebraic solution, the two y value are equal so
equate the right hand sides of the expressions and solve for x:
-5 + 2x = 30 – 3x We want term in ix on the left-hand side but not on the right, so add 3x to both sides since -3x + 3x = 0. We then have:
-5 + 2x + 3x = 30
or -5 + 5x = 30
To remove the constant term from the left side we now add 5 to each side, giving:
Lines intersect at (7, 9)
5x = 35
And so, dividing by 5, we have x = 7
We then find the value for y by substi tuting x=7 in either of the equations. Using y=30 – 3x gives:
y = 30 – 21 = 9
Which confirms the graphical
SOLUTION IN TERMS OF OTHER
VARIABLES
Not all the equations you deal with have numerical solutions.
Sometimes when you solve and equation for x you obtain and expression containing other variables.
Use same rules to transpose the equation.
Remember that in the solution x will not occur on the right-hand side
and will be on its own the left-hand side.
If you are given a relationship in the form y=f(x), rewriting the
equation in the form x=g(y) is called finding the inverse function.
To be able to find the inverse there must be just one x value
corresponding to each y value.
For non linier function there can be difficulties in finding an inverse,
but we may be able to do so for restricted set values.
The function y=x2 has two x values (one positive and one negative)
corresponding to every y value, but if we consider the restricted function y=x2, x>0 this function has the inverse x=y.
For the linier functions often use in economic models inverse functions
can always be found. One reason for finding the inverse function can always be found. One by y is conventionally plotted in economic on the horizontal axis.
Solve for x in term of z
x = 60 + 0.8x + 7z
At first glance you seem to already have a solution for x, but
notice that x occurs also on the right-hand side of the
equation. We must collect terms in x on the left-hand, so we subtract 0.8x from both sides and obtain:
x - 0.8x = 60 + 7z
since both left-hand side terms contain x we may write: (1 – 0.8)x = 60 + 7z
which gives
0.2x = 60 + 7z
To get x with a coefficient of 1 we divide both sides by 0.2 = 1/5, which is the same thing as multiplying both sides by 5. This gives:
Given y = x + 5, obtain an expression for x in term of y.
Begin by interchanging the side so that the sides with x is on
the left of the equation. We then have:
x + 5 = y
Next subtract 5 from both sides, giving:
x = y – 5
To find x we must square both sides. This means that the whole of the right-hand side is multiplied by itself, so use brackets. We obtain:
x = (y – 5)2
SUBSTITUTION
When two expression are equal to one another, either can
be substituted for the other.
The technique is used the effect of the imposition of a per
unit tax on a good and to solve simultaneous equations.
When substituting, always be sure to substitute the whole
of the new expression and combine it with the other term in exactly the same way the expression it replaces was
combined with them.
For example, if y = x2 + 6 and x = 30 - , find an
expression for y in term of . Substituting 30 - for x we
obtain:
y = (30 - )2 + 6
DEMAND AND SUPPLY
Demand and supply function in economics express
the quantity demanded or supplied as a function of price, Q = f (P).
According to mathematical convention the dependent
variable (Q) should be plotted on the vertical axis.
Economic analysis, however, use the horizontal axis
as the Q and for consistency we follow that approach. So that we can determine the points on graph in the usual way, before plotting a demand or supply
Find the inverse function for the demand equation Q = 80 – 2P
and sketch the demand curve.
Adding 2P to both sides of the demand equation we get
2P + Q = 80
Subtracting Q from both sides we obtain: 2P = 80 – Q
Dividing each side by 2 gives the inverse function P = (80 – Q)/2 = 40 – (Q/2)
The demand function is linier, so it suffices to plot two point. Selected values of Q are shown in the table together with corresponding value for P.
Q 0 20 40 60 80
MARKET EQULIBRIUM
Market equilibrium occurs when the quantity supplied
equals the quantity demanded of a good.
The supply and demand curves cross at the equilibrium
price and quantity.
If you plot both the demanded and supply curves you
can of approximate equilibrium values from the graph.
Another approach is to solve algebraically for the point
where the demand and supply equation are equal. This gives exact value. Suppose we wish to find the
equilibrium price and quantity when demand is given by
Demand: Q = 96 – 4P And the supply equation is
For an algebraic solution we can use the equation in this form.
Since in equilibrium then quantity supplied equals the quantity demanded, the right-hand side of the supply equation must
equal the right-hand side of the demand equation. This gives an equation in P:
Supply Q = Demand Q (in equilibrium), so 8P = 96 – 4P
Adding 4P to both sides gives 12P = 96
Dividing by 12 we find P = 8 which is the equilibrium price. We can then substitute this into either equation, say the equation. This gives:
Q = 8 x 8 = 64
Jawaban QUIS I
1. Sketch the total cost function: TC = 300 + 40Q – 10Q2 + Q3,
write expressions for AC, FC, VC and AVC !
AC = 300/Q + 40 – 10Q +
Q2
FC = 300
VC = 40Q – 10Q2 + Q3
AVC = 40 – 10Q + Q2
TC=3 00+4
0Q
-10Q
2+Q 3
Q 0 1 2 3 4 5 6 7 8 9 10 11 12
Jawaban QUIS I
3. A firm in perfect competition sells it output at a price Rp 12. Plot it total revenue function (TR) = 12Q !
Price constant, TR a line through the origin
