
Differentiation in Economics – Objectives 1. Understand that differentiation lets us identify marginal relationships in economics Measure the rate of change along a line or curve Find d y /d x for power functions and practise the basic rules of differentiation
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denoted
should be regarded as a single symbol and you should not try to work separately with parts of it
is an expression that measures the slope of the tangent to the curve at any point on the function y = f(x)
is itself a function of x
for any particular x value by substituting that value of x
D y = Dx.
Constants differentiate to zero, i.e. if y = c where c is a constant
= 0
= n.axn–1
Constant Times a Function Rule
=
= x – n
x = x0.5 = x1/2
=
=
= m
= m
=
1. Write down the equilibrium condition for the economy
Y = AD
Income = Aggregate Demand
2. Write an expression for AD
AD = C + I + G + X – Z
Substitute into this, but do not substitute a numerical value for the autonomous expenditure I so
AD = f(Y, I)
Substituting AD in the equilibrium condition gives an equation where Y occurs on both sides
3. Collect terms in Y on the left-hand side and solve for Y
4. Now differentiateIf Y = income and I = investment dY/dI is the investment multiplier
before at critical value after
of the function we differentiate that and the result is called the second derivative of the original function
=
a maximum from a minimum
Maximum Minimum
0 0
– ve +ve
Total Inventory Cost =
set = 0 for a minimum
and maximum total revenue occurs when E = – 1
MVP = P.MPL is the marginal value product of labour