## Demand functions: How to read?

In our last quiz, we saw some demand equations with questions on elasticity, inferior/normal good, complimentary or substitute good, etc. Here I’ll explain how to deduce these from a demand equation. It was horrifying to look at complex equations, with an expectation to understand them, and then derive conclusions. On googling around, I found out that the rules are generic, and can be applied to any equation, given that the micro economics basics are clear. It boils down to common sense finally.

Lets define few things first:

Price Elasticity: If demand increases/decreases a lot more than price decrease/increase respectively, then it’s termed as more elastic. Lets say insulin, demand will not decrease if price increases, as there’s no substitute, hence it’s inelastic. Take coffee, demand will decrease much more than price increase, as there are many substitutes in place.

Complementary/ Substitute: This is self explanatory. Tea and coffee are substitutes. Tea and biscuits are complementary.

Inferior/Normal Good: If users stop using a particular good when their income increases, it’s termed as inferior good. On other hand, if demand of a particular good increases with increase in income, it’s a normal good. Examples, Hyundai Santro is an inferior good, as with more income I’ll buy Fortuner 🙂 . Gold is a normal good( in fact more than normal). If my income rises, I buy more.

Coming to equation:

Q = 100Px(-1.2) Pz(0.5) Y(0.7)

Q = Quantity demanded for X

Px = Price of X

Pz = Price of good Z

Y is the income

Is it price elastic or inelastic?

We see that Q is inversely proportional to Px, which is true for demand function. Now, lets make Px double i.e. Px = 2 Px. Other things equal, quantity demanded will decrease by 2(1.2) times, which is more than 2. Hence change in quantity > change in price, so this is price elastic.

Is Z a substitute or complement?

Increase price of Pz and you can see that quantity demanded for X will also increase. It means that X and Z are substitutes. On increasing price of Z, people are substituting it with X, and hence demand of X is increasing.

Is X inferior or normal good?

Increase the income, and you will see demand of X is rising. So it’s a normal good. Had it been inversely proportional, story would have been different.

Hope above was a simple analysis, and can be applied to any demand equation.

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## Demand Elasticities

It’s a measure of sensitivity of the Quantity demanded vis a vis changes in price. In simple words, does quantity change too much or too little on increase/decrease in price.

Mathematically,

E(d) = (Delta)Q/Q     ÷  (Delta)P/P

So,

E(d) >1 : If percentage change in quantity > percentage change in price, it’s called “Elastic” Demand. For ex, demand of air travel will decrease quite a bit with increase in price, and people may prefer trains or other means of transportation, and vice versa for decrease in price.

E(d) < 1: If percentage change in quantity < percentage change in price, it’s called “Inelastic” Demand. For ex, demand for oil is inelastic, as demand of oil doesn’t vary much with price.  As there are not many substitutes available. Other example is demand for insulin doesn’t change, and remains same, as there’s no other alternative.

E(d) = 0 : This is case of perfect inelastic demand. Quantity doesn’t change at any price.

E(d) = ∞ : This is case of perfect elastic demand. Small variations in price leads to huge changes in the quantity.

Elasticity of a product can be calculated from all the historical data, and is helpful in determining the future prices in case production increases or falls. For example, when oil producing countries go out to decrease the production, what will be its effect on price, etc.

Revenue projections w.r.t Elasticity:

Revenue is Price x Quantity Demanded.

If E(d) >1, then increase in price by x%(say 10%) will decrease in quantity demanded by more than x % (say 20%).

So old revenue = PQ

New revenue = (1.1)P x (0.8)Q = 0.88 PQ , so total effect is that revenue got decreased.

If E(d) <1, then increase in price by x%(say 10%) will decrease in quantity demanded by less than x % (say 5%).

So old revenue = PQ

New revenue = (1.1)P x (0.95)Q = 1.045 PQ , so total effect is that revenue got increased.