1. Academic Year: 2012/2013
Instructors: Brenda Lynch and PJ Hunt
Contact: brendalynch@ucc.ie
p.hunt@ucc.ie

2. Income elasticity
Formula % ∆ Qd
%∆Y
 Example: Qd of coal is 9 ton/hour, then
income rises from €475 to €525pw and Qd
of coal rises to 11 ton/hour. Calculate Yd.

3.  Change in Qd is 2, original quantity is 9
giving 2/9. Change in income is €50,
original income is €475 giving €50/€475.
 The income elasticity of demand for coal
is 2/9 = 2.11
50/475

4.  Yd Greater than 1 (demand is elastic,
normal good, Luxuries)
 Yd Positive and less than 1 (demand is
inelastic, normal good, Necessities)
 Yd Negative (inferior good)
 Cross Price Elasticity
 Formula % ∆ Qda
% ∆ Pb

5. And is the % change in demand for good A
caused by the % change in price of good B.
If good B is a substitute for good A, A’s
demand will rise as B’s price rises and CED
will be a positive figure.
If good B is a compliment to good A, A’s
demand will fall as B’s price rises and CED
will be negative.

6. The major determinant of CED is the closeness of
the substitute or compliment. The closer it is the
bigger will be the effect and hence the greater
the CED – either positive or negative.

7. Example: Demand equation for a product is:
Qd = 90 – 8P + 2Y + 2Ps/c
where P = 10, Y = 20 and Ps/c = 9
Find Ed, Yd and CED.
 Is the demand for the product inelastic or
elastic?
 Is it a normal or inferior good?
 Is the product a luxury or a necessity?
 Does the product have a close substitute or
compliment?

8. First find a value for Qd. Substitute in the given
values for P, Y & Ps to the equation.
 Q = 90 – 8(10) + 2(20) + 2(9)
Q = 68
Now calculate each elasticity using the
following formulae

9. Ed = (ӘQ/ ӘP)(P/Q) = -8(10/68) = -1.18
Inelastic or elastic?
Yd = (ӘQ/ ӘY)(Y/Q) = 2(20/68) = 0.59
Necessity or luxury, normal or inferior?
CED = (ӘQ/ ӘPs/c)(Ps/Q) = 2(9/68) = 0.26
Substitute or compliment, close or not?

10. Total Revenue (TR)
Determine from the demand function Q =
100 - P that MR is zero when TR is
maximised at unit elasticity.
Rearrange equation to get P = 100 - Q
TR = P*Q, TR = (100 – Q) * (Q).
So TR = 100Q – Q2

11. MR = ∆TR / ∆Q = 100 – 2Q. TR is maximised
when MR = 0
Set MR = 100 – 2Q = 0. Q = 50
Recall: P = 100 – Q(50) P = 50
So TR is maximised when P = 50 and Q = 50

12. Ep = ∆Q/∆P * P/Q
∆Q/∆P = first derivative of P = 100 – Q = -1
EP = -1(50/50) = -1
so Ep = -1 where MR = 0 and TR is
maximised.