Question

Generalize the formula for excess burden when supply curve is perfectly elastic to the case where supply curve is upward sloping and the elasticity of
supply is n. Show buyers price increases by n/(n+e)*tbPb and sellers price decreases by e/(n+e)*tbPb
Derive the change of quantity traded from it.

Answer 1

Price Elasticity of Supply

We have been studying the impact of price on supply. However, all these definitions have been qualitative. With this in mind, the price elasticity of supply came into existence. The price elasticity of supply tackles the quantitative side of the price and supply relationship.

It refers to the degree of responsiveness of supply of a commodity with reference to change in the price of such commodity. Note that the price elasticity of supply is always positive. This happens because of the positive or direct relationship between price and supply, unlike demand.

Measurement of Price Elasticity of Supply

We can measure price elasticity of supply using the following two methods:

Percentage Method

The percentage method is the most frequently used method to calculate the price elasticity of supply, as was in the case of demand. This method is also known as the proportionate method. According to this method, elasticity is measured as the ratio of the percentage change in the quantity supplied to a percentage change in the price. The formula to calculate the price elasticity of supply using percentage method is as follows:

Es= Percentage change in quantity supplied/ Percentage change in price

Here,

Es= The price elasticity of supply,

Percentage change in quantity supplied= [ Change in quantity supplied/ Initial quantity supplied]×100

Percentage change in price= [Change in price/Initial price]×100

The Proportionate Method: The percentage method rightly also known as the proportionate method as the formulas for both are interchangeable and one can easily derive the other. Considering and putting the following values in the formula for percentage method: Let change in quantity supplied=ΔQ, initial quantity= Q, change in price=ΔP, initial price= P, we get:

Es= { [ΔQ/Q)×100] ÷ [(ΔP/P)×100] }

= (ΔQ/ΔP)×(P/Q)

Geometric Method

The geometric method helps in calculation of price elasticity of supply from the supply curve itself. This method is based on the viewpoint that elasticity can be calculated at a point on the supply curve. It is also known as the point method or the arc method. The formula to calculate elasticity using this method is as below:

Es= Intercept of supply curve on the X-axis/ Quantity supplied at that price

Kinds of Elasticities of Supply

(Source: economicsonline)

According to the market for commodities, they respond differently to changes in price. These different reactions are mapped using the concept of price elasticity if supply. According to the different kinds of responsiveness of commodities, the price elasticities of supply are categorized into five types.

Perfectly Elastic Supply

A commodity is said to have a perfectly elastic supply if it has an infinite supply at a particular price and even a slight change in this price brings the supply down to zero. This further means that any quantity of the commodity can be supplied at this price and suppliers refuse to supply even one unit at any rate different from this price.

Under these circumstances, the price elasticity of supply Es is equal to ∞. Further in geometric terms, a supply curve with a horizontal straight line parallel to the X-axis exhibits the behaviour of a perfectly elastic supply.

Perfectly Inelastic Supply

A perfectly inelastic supply remains unmoved in response to any change in the price. In other words, the supply of such a commodity always remains constant no matter what the price is. A perfectly inelastic supply is represented as Es= 0. Further, a perfectly inelastic supply curve is a vertical straight line parallel to the Y-axis.

Highly Elastic Supply

When percentage change in quantity supplied is more than the percentage change in price then the supply is said to be highly elastic. Alternatively, the supply of such a commodity has a high degree of responsiveness or is volatile. The supply responds by a big factor for even a small change in the price. The price elasticity of supply for such a case is greater than 1, i.e. Es>1 and the supply curve has an intercept on the Y-axis or a negative intercept on the X-axis.

Less Elastic Supply

For a less elastic supply, the percentage change in quantity supplied is smaller than the percentage change in price. The supply for such a commodity tends to change by a small factor and has a small degree of responsiveness to a change in the price. In this case, the price elasticity of supply or Es<1 and the supply curve has an intercept on the X-axis.

Unitary Elastic Supply

When percentage change in quantity supplied is equal to the percentage change in price such that the price elasticity of a supply is equal to one, then supply for such a commodity is said to be unitary elastic. As mentioned, in such a case Es= 1. Further, the supply curve is a straight line passing through the origin. Note that any supply curve that passes through the origin, irrespective of its slope, tends to have a unitary elastic supply.

Time Period and Supply

The change in the supply of a commodity also depends on our perception of the timeframe. This means, that in many cases the change in supply tends to differ when considered over different time periods. Such an observation leads to a classification of time into three time periods.

• Market Period: A market period is a very short interval of time. On the other hand, supply cannot change in the blink of an eye. Producers need time to adjust to the changes in the price of a commodity. Observe that such statements are similar to the conditions of a perfectly inelastic supply. Thus, in a market period, the supply is perfectly inelastic.
• Short Period: A Short period is a small period of time. In such a timeframe, only the variable factors of production can be played with. Hence the change in supply is limited to a small degree of response. Evidently, for a short period, the supply tends to be less elastic.
• Long Period: A long period of time is a time interval sufficiently long, in which all the factors of production can be altered. Thus for a long period, the supply responds in a high manner.

Factors that Govern Price Elasticity of Supply

Nature of the Commodity

On the basis of nature of commodities can be classified into durable or perishable goods. Definitely, their response to a change in price also varies. Durable good has long lifetimes and can be stored for long periods. Examples are furniture, TV etc. Hence such goods have high elastic supply as producers can manipulate their supply to earn greater profits.

On the other hand, perishable goods have short lifetimes and cannot be stored. Vegetables, milk etc are some perishable goods. Such goods need to be disposed off and hence have an inelastic supply.

Cost of Production

As a firm looks to expand production, it needs to employ more factors of production. As a result of this, the cost of production rises. This rise varies from one factor to another factor of production. If the cost of adding more factors of production rises rapidly then the firm refrains from expanding supply.

Conversely, a slow rise in the cost of production with the addition of factors proves to be a good incentive for change in supply. Thus, the supply is inelastic in former various it tends to be elastic in the latter.

Time Period

As already discussed, in market period supply is inelastic, in short, time period supply is less elastic whereas in a long time period supply tends to be more elastic.

Nature of Inputs Used

The elasticity of supply depends on the nature of inputs. Inputs can be divided as easily available and scarcely available. If the inputs are easily available then the supply is elastic as it can be changed easily. On the other hand, if the availability of inputs is scarce then the supply tends to be inelastic.

Natural Factors

The commodities, whose production is dependent on natural factors, as in case of seasonal crops, have an inelastic supply. On the contrary, goods whose production is independent of natural factors for example manufactured goods, have an elastic supply.

A Solved Example for You

Q: Why is the price elasticity of supply always positive?

Ans: The price elasticity of supply is always positive because of the direct relationship between price and quantity of a commodity supplied. In other words price and supply move in same directions