Question

Compare the price elasticities of demand at every price for the two demand curves: x1 = 450 - p1 and x1 = 150 - 1/3 p1. Explain your answer using a graph.

Answer 1

In the above question, there are two demand equations

x1 = 450 - p1

and

x1 = 150 - 1/3 p1

We have both equations so we can find values by inserting different values

For eg - if we take quantity as 10 units in the equation x1 = 450 - p1 so the price will be

10 = 450 - P

P = 440

Units	Price (x1 = 450 - p1)	Elasticity	Price (x1 = 150 - 1/3 p1)	Elasticity
20	430	--	390	--
40	410	21.5	330	6.5
60	390	10.2	270	2.7
80	370	6.4	210	1.5
100	350	4.6	150	0.8
120	330	3.5	90	0.5
140	310	2.7	30	0.2

In the above elasticity is calculated on every price by percentage method

like when the quantity is increased from 20 to 40 and price is decreased from 430 to 410 then price elasticity of demand will be 21.5

after this

when the quantity is increased from 40 to 60 and price is decreased from 410 to 390 then the price elasticity of demand will be 10.5

similarly, all values are calculated.

Now from the above table if we look at elasticity columns of both equations

we can see that at every price, elasticity of x1 = 450 - p1 is greater than x1 = 150 - 1/3 p1

Also if we draw both the demand curves

We can clearly see that the demand curve of x1 = 450 - p1 is flatter whereas the demand curve of x1 = 150 - 1/3 p1 is steeper

Flatter curve shows a high elastic demand curve and steeper curve shows less elastic demand curve