Worked Examples for Elasticity Formulas

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Question

A consumer buys 5 units of a good per week when their weekly income is 250.

When their weekly income increases to 280, they buy 7 units of the good.

Calculate the income elasticity of demand for this good.

Workings

We need to use the YED formula

\[\frac{\[\frac{(Change in Q)}{.5(Q1 + Q2)}\]}{\[\frac{(Change in Y)}{.5(Q1 + Q2)}\]}\]

Here:

Change in Q = +2 (7-5)

Q1 = 5

Q2 = 7

Change in Y = +30 (280-250)

Y1 = 250

Y2 = 280

Putting these figures into the formula, we get:

[(2) / .5(5 + 7)] / [(30) / .5(250 + 280)]

Simplifying it down..

> [2/12] / [30/265]

> (0.167) / (0.113)

> 1.478

Worked Examples for Calculating YED & PED

Example 1 - YED

Example 2 - CED

Question

When the price of good X is 27, the quantity demanded of good Y is 1,200 units.

When the price of good X falls to 23, the quantity demanded of Good Y falls to 800 units.

(i) Calculate the Cross Elasticity of Demand for Good Y

(ii) Is Good Y a substitute for or a complement to Good X?

Workings

(i) We need to use the CED formula

\[\frac{\[\frac{(Change in Q(X))}{.5(Q1(X) + Q2)}\]}{\[\frac{(Change in P(Y))}{.5(P1(Y) + P2(Y))}\]}\]

Change in Q(X) = -400

Q1(X) = 1,200

Q2(X) = 800

Change in P(Y) = -4

P1(Y) = 27

P2(Y) = 24

Putting these figures into the formula, we get..

[(-400) / .5(1,200 + 800)] / [(-4) / .5(27 + 24)]

> [-400/1,000] / [-4/25.5]

> -0.4/-.157

> 2.5

(ii) Good Y is a substitute good because the CED is positive.

This means that as the price of Good X fell, consumers switched from the dearer Good Y to the cheaper Good X

Elasticity Worked Examples