# Demand Function

Determination of Price Elasticity from a Demand Function

Illustration 1

Presume the price of a product drops from \$12 to \$8 per unit and due to this quantity demanded of the product enhances from 160 units to 240 units. Determine the price elasticity of demand.

Solution

Variation in the demand of quantity (Q2 – Q1)

Percentage change in demand of quantity      =     Q2 – Q1 * 100
Q2 + Q1
2

=          240 – 160 * 100
240 + 160
2

=          80 * 100          =          40
200

Change in Price                                   =          P2 – P1

=          8 – 12

Percentage change in Price                 =       P2 – P1 * 100
P2 + P1
2

=          8 – 12  * 100
8 + 12
2

=          – 4 * 100          =          – 40
10

Price Elasticity of Demand                 =          % change in quantity demanded
% change in price

=          40                    =          – 1
– 40

Disregarding the negative sign, the price elasticity of demand parities to zero.

Illustration 2

Presume a seller of a silk fabric necessitates lowering the price of its cloth form \$180 per metre to \$ 175 per metre. If its present sales are 1500 metres per month and moreover it is evaluated that its price elasticity of demand for the commodity is equal to 0. Determine the following.

Whether or not his total revenue will enhance as a consequent of his judgement to lower the price and

Compute the exact enormity of its fresh total revenue.

Solution

(1) Price Elasticity of a demand function       =      Δq                    p
Δp        *          q

Here, p = \$180, q = 1500 metres,

Δp = 180 – 175 = 5; Δq = not known; price elasticity of the product ep = 0.5

Substituting the values of p, q, Δp and ep in the price elasticity standard formula, we procure,

0.5       =         Δq                    180
5          *          1500

Δq        =          0.5 * 5 * 1500
180

=          3750
180

Δq       =          21

As the price had dropped the quantity demanded will enhance by 21 metres and hence the new quantity sold per month would be 1500 + 21 = 1521 metres.

(2) Total Revenue before discount in price

=          1500 * 180      =          \$270,000

Total Revenue after price discount will be

=          1521 * 175      =          \$266,175

Therefore, the discount in price has enhanced sales total revenue of the seller.

Ascertaining Cross Elasticity of from a Demand function – Using Mid Point Method

Illustration 3

If price of green tea hikes from \$75 per 250 grams to \$85, results the consumer demand for ordinary tea enhances from 800 packs to 1000 packs of 250 grams pack then ascertain the cross elasticity of demand of green tea and ordinary tea.

Solution

Change in quantity demanded of ordinary tea=         Qot2 – Qot1

=          1000 – 800      =          200

Change in price of green tea                        =          Pgt2 – Pgt1

=          85 – 75            =          10

Substituting the values of the various variables in the cross elasticity of demand formula of midpoint method;

Cross Elasticity of Demand    =         1000 – 800      /           85 – 75
1000 + 800      /           85 + 75
2                               2

=          200      /           10
900      /           80

=          200      *          80
900                  10

=          1.78

Illustration 4

Presume the demand function for green tea in terms of price of ordinary tea is provided. Determine the cross elasticity of demand when price of ordinary tea hikes from \$40 per 250gms pack to \$50.

Qgt      =          200 + 2.5P ot, where Qgt is the quantity demand of green tea in terms of 250 grams pack and P ot is price of ordinary tea.

Solution

The plus sign of the co-efficient of P ot depicts that hike in price of ordinary tea will cause an enhancement in demand of quantity of green tea. This entails that ordinary tea and green tea are substitutes.

The demand function entails that co-efficient      d Qgt   =          2.5
d P ot

With a view to ascertain cross elasticity of demand among ordinary tea and green tea, we must first ascertain quantity demand of green tea when price of ordinary tea is \$40 per 250 grams. Therefore,

Qgt      =          200 + 2.5 * 40

=          200 + 100        =          300

Cross elasticity            ec         =         dQgt                Pot
dPot    *          Qgt

=          2.5       *          40
300

=          0.33

Illustration 5

Let us assume the demand function of oil in a metropolitan city Q = 1500 – 15P, Q is in thousands of litres. It is necessary to ascertain the price elasticity at price of \$25 per litre.

Solution

ΔQ       in the provided demand function is 15. To procure price elasticity we have
ΔP       first to compute the demand quantity at the provided price of \$25 per litre.

Substituting the 25 for P in the provided demand function we procure,

Q         =          1500 – 15 * 25

=          1500 – 375

Q         =          1125

Now substituting the P = 25 and Q = 1125 and ΔQ            = 15 in the elasticity expression
ΔP

of function ΔQ * P
ΔP      Q

ep        =          15 *  25
1125

=          0.33.

Therefore, the price elasticity at price \$25 per litre is 0.33 and quantity demand of oil parities 1125 thousand litres.