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.
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.
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.
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.
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%.
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.
