Question

Jilly sells ice cream at the beach. You have determined that demand can be described by the following demand equation: Q = 1,200 - 200P. a. If P = $3.00, determine the number of ice cream sold and the elasticity of demand at this price. b. If price is increased to $4.00, determine the elasticity of demand at this new price. Is demand more or less elastic after the price increase?

Answer 1

Answer

Given we have

Demand equation

Q = 1,200 - 200P (i)

The price elasticity of demand is defined as the % change in the demnaded quantity

Mathematically it is given by

---------------------equation (ii)

Remember the negative value of E comes from dp/dq whihc is basically the slope of the demnad curve equation whihc is a negative number according to the law of demands implication .

When | E | > 1 the price of demand is elastic

| E | < 1 the demnad price is inelastic

| E | = 1 the price of demnad is unit elastic

a.

Given P= $ 3

Therefore computing the price elasticity of demand of the given problem

Q = 1,200 - 200P

Taking the differentation dq with repect to dp we get

dq/dp = -200

substiuting the values in equation (ii) we get

E = (P/ 1200- 200P ) ( -200)

E = P/P-6 ---------------------------euqation ( iii)

Now we have P = $ 3

E = 3/ 3- 6 = -1

Hence the demand elasticty of price is -1

& | - 1 | = 1

whihc implies unit price elastic demand

Accoridng the the condition mentioned above for demnad elasticity if |E| > 1 then the price is unit elastic price .Therefore the price is unit price elastic

b. if P= 4 $

then substituitng in equation (iii) we get

E = P/P-6

E = 4/4-6

E = -2

| -2 | > 1

which implies the ice cream price is elastic , and management should consider lpweiring the price to rasie the revenue