Answer to Question #248332 in Macroeconomics for hlulaks

Question

You have recently received a report from the Chief Finance Officer (CFO) indicating that the price elasticity of demand for the electronic equipment is 1. 6. Advise the CFO on what the figure 1.6 means and explain the relationship between price elasticity of demand and total revenue. (Use relevant diagrams to explain your answer)

Answer 1

To explain the price elasticity of demand first we need to discuss the law of demand: the demand for any good varies negatively with price that is, as price of a product rises, the demand for that particular product falls keeping other factors(like, consumer's taste & preferences, population size, income distribution of the economy, price of related products, advertisement etc.) of demand constant.

Price elasticity of the product tells us how much demand of that product may change due to rise in price of that product. Formally, price elasticity of demand is the percentage change in quantity demanded divided by percentage change in price of that product. So, the price elasticity of demand of electronics equipment is 1.6 implies that, if price of electronics equipment rises by 1 unit then the quantity demanded will fall by 1.6 units that is, quantity demanded will fall more than proportionately compare to rise in price that implies the product have elastic demand(that is, quantity fall more than rise in price).

The price elasticity of demand equation can be written as:

$|e|= \frac{-(∆Q/Q) \times 100}{(∆P/P) \times 100}$

Or

$|e|= \frac{-(Q-Q')/Q}{(P-P')/P}$

(From the graph above, where the DD' is the downward sloping demand curve. If we move along the curve from A to B the price falls and quantity demanded rises).

The negative sign is added to make the whole expression positive as demand curve is negatively sloped.

Note the graph above, as we move from point A to B, the total revenue that is price level multiplied by the total quantity demanded(assuming that what's demanded can be supplied in the market) also changes. At point A, TR was area OPAQ and at point B it becomes OP'BQ'.

TR=PQ

To know whether the change in price is good for the business that is the change in price increases the TR or not we can take partial derivative of TR with respect to P and find out the relation between change in TR due to change in P and |e|:

TR=PQ

$\frac{dTR}{dP} = \frac{dQ}{dP}P +Q \\ = Q(1 + \frac{dQ}{dP} \times \frac{P}{Q}) \\ = Q(1 -|e|)$

So, if |e| <1

Q(1-|e|)>0

If |e|> 1

Q(1-|e|)<0

Note that, if |e|>1 (1.6>1) then Q(1-|e|)<0 that is, change in TR due change in ap is negative. So if the product has inelastic demand, price rise will reduce the total revenue.