Price elasticity of demand and total revenue

[Nanda]

PED=(%change in QD)/(%change in P)

Suppose, initial QD=1000 and %change in QD= -13% = -0.13
and initial P=10 and %change in P= 14% = 0.14

Therfore, absolute value of PED = .13/.14 < 1, which implies the demand is inelastic at that particular point.

Since it is inelastic at that particular point, so the total revenue(TR) must increase.

Initial TR=1000*10=10000
Final TR=1000(1-.13)*10(1+.14)= 9918.

(Means the TR decreased when price is increased)

Here the total revenue decreases. (Kindly rectify me if I am wrong anywhere)


If all my above steps were correct, how can the statement be justified which states, that an inelastic demand curve will have incerased TR when price is increased.

 

[cjno1]

Since it is inelastic at that particular point, so the total revenue(TR) must increase.

All your figures are right, but the above statement is where you've got mixed up a little. You are saying that for a price inelastic good, if you drop the price total revenue should increase, it's actually the other way around!

Take an extreme example, a good with a price elasticity of 0. In other words, it doesn't matter what I change the price to, quantity demanded will stay exactly the same. In this instance it's clear to see that if I drop my price, my total revenue must decrease, because I'm selling the same quantity at a lower price.

This holds true for all price inelastic goods.

 

[Graham Aylott]

Yes, if demand is inelastic, then a given percentage decrease in price will lead to a smaller percentage increase in quantity and so total revenue (= price x quantity) will fall.

 

[Sarahlouise_23]

I don't think I understand the answer to this question. I thought that if PED < 1 then as P decreases, TR will decrease and as P increases, TR will increase. Hasn't P increased in the example given?

 

[Nanda]

I don't think I understand the answer to this question. I thought that if PED < 1 then as P decreases, TR will decrease and as P increases, TR will increase. Hasn't P increased in the example given?

For an inelastic demand curve, a fall in price would result in a smaller % rise in quantity demand. Hence TR will fall.

Similarly, for an inelastic demand curve, a rise in price will result in a smaller fall in QD and hence the TR will also rise.

There is also formula which show that same result.

 

[Sarahlouise_23]

I understand the theory but I don't understand in relation to the example given. Hasn't P increased in the example given? I thought P had increased by 14%.

 

[Nanda]

Yes.....P increased by 15% in the given example.

 

[Graham Aylott]

TR = P*Q

Differentiating this partially with respect to Q gives:

dTR/dQ = P*1 + dP/dQ * Q

So, remembering that MR is the derivative of TR and dividing each term on the right-hand side by P gives:

MR = P*(1 + dP/dQ * P/Q) = P*(1+1/e)

where e = price elasticity of demand.

So, from this you can see that if -1 < e < 0 (inelastic demand), then MR < 0, ie an increase in Q resulting from a fall in P will result in a fall in TR.

Conversely, if e < -1 (elastic demand), then MR > 0, ie an increase in Q resulting from a fall in P will result in a rise in TR.

However, this mathematical result (based on derivatives) applies only to small changes in P and hence Q.

If the percentage changes in P and Q are very similar (ie demand is only "slightly inelastic") and quite large, as in the original example, then the above mathematical result won't always apply.

For example, if P increases by 1.4% and Q decreases by 1.3%, ie small changes, then:

TR = 10.14 * 987 = 10,000.18 > 10,000 so it does hold.

If, however, P increases by 14% and Q decreases by 13%, ie "large" changes (as per the original example) then:

TR = 11.4 * 870 = 9918 < 10,000

So, if asked in the exam, we will always say that inelastic demand means that a fall in P leads to a smaller percentage rise in Q and so (intuitively) it leads to a fall in TR = P * Q. However, in the real world, it's not always that straightforward.

 

[Sarahlouise_23]

Thank you Graham, that's really helped!