[Economics HW] HELP! If the demand for a good is inelastic and the price of the good decreases,?

Question

This is my econ HW.

Please guide me for the correct answer!

If the demand for a good is inelastic and the price of the good decreases,

A. total revenue increases.

B. total revenue decreases.

C. total revenue is not affected.

D. the direction of the change in total revenue cannot be determined from the information given.

Thanks for your help!!!

Answer 1

The correct answer is: A. total revenue increases.

It is easy to see that.

Inelstic price elasticity of demand means that if prices changes by (say) x %, demand will change in the opposite direction by less than x%. Since total revenue is the product of demand and price, this in turn means that total revenue will be higher. Here the concept of price inelasticity is that price elasticity of demand is <1.

So, R = P*Q where R is revenue, P is price and Q is quantity of demand.

taking differentiation with respect to  P, we get

dR/ dP = Q + P *dQ/dP. = Q [ 1 + (dQ/dP) / (P/Q)] = Q(1+e), where e is the price elasticity of demand = (dQ/dP) / (P/Q).

Now  change in Revenue following a price change

= dR/dP = Q(1+e). But price elasticity of demand is negative but less than 1 (unity) in absolute terms. So, 1+e is one minus something less than one and hence a positive value. Q is also positive value. So Q(1+e) is a positive value. This means change in revenue following a price change is positive in the case of price inelastic demand ( absolute value of e< o, or -1<e<0.

Answer 2

The answer here is simple. Lets look at the activity in question. You are talking about an inelastic good which means that the demand for this good is in constant demand under most circumstances. The price is X amount and people are prepared to pay this price no matter what. Lets take cigarettes and alcohol as examples, people buy them at any price. The company's who produce these products make a certain amount of revenue from the sales at a certain price. If this price were to be lowered the revenues would decrease. Magic!

Answer 3

Total revenue decreases since you won't sell more by lowering the price, and you get less for the ones you do sell.

Answer 4

B. total revenue decreases.

It's base of elasticity concept. E=ΔQ%/ΔP% and inelastic demand means that:

| E | <1

And since conclusion from above is: ΔQ% < ΔP% and total revenue defined as TR=Q*P so P will fall faster than Q rises.