Q. Explain the relationship between revenue concepts and price elasticity of demand.
Relationship between Revenue Concepts and Price Elasticity of Demand
Elasticity of Demand, Average Revenue and Marginal Revenue
There is a very useful relationship between elasticity of demand, average revenue and marginal revenue at any level of output. Elasticity of demand at any point on a consumer’s demand curve is the same thing as the elasticity on the given point on the firm’s average revenue curve. With the help of the point elasticity of demand, we can study the relationship between average revenue, marginal revenue and elasticity of demand at any level of output.
In the diagram AR and MR respectively are the average revenue and the marginal revenue curves. Elasticity of demand at point R on the average revenue curve = RT/Rt Now in the triangles PtR and MRT.
tPR = RMT (right angles)
tRP = RTM (corresponding angles)
PtR= MRT (being the third angle)
Therefore, triangles PtR and MRT are equiangular.
Hence RT / Rt = RM / tP
In the triangles PtK and KRQ
PK = RK
PKt = RKQ (vertically opposite)
tPK = KRQ (right angles )
Therefore, triangles PtK and RQK are congruent (i.e., equal in all respects).
Hence Pt = RQ
Elasticity at R = RT / Rt = RM / tP = RM / RQ
Hence elasticity at R = RM / RM – QM
It is also clear from the diagram that RM is average revenue and QM is the marginal revenue at the output OM which corresponds to the point R on the average revenue curve. Therefore elasticity at R = Average Revenue / Average Revenue – Marginal Revenue
If A stands for Average Revenue, M stands for Marginal Revenue and e stands for point elasticity on the average revenue curve Then e = A / A – M.
Thus, elasticity of demand is equal to AR over AR minus MR.
By using the above elasticity formula, we can derive the formula for AR and MR separately.
eA – eM = A bringing A’s together, we have
eA – A = eM
A ( e – 1 ) = eM
A = eM / e – 1
A =M (e / e – 1)
Therefore Average Revenue or price = M (e / e – 1)
Thus the price (i.e., AR) per unit is equal to marginal revenue x elasticity over elasticity minus one. The marginal revenue formula can be written straight away as
M = A ((e – 1) / e)
The general rule therefore is: at any output,
Average Revenue = Marginal Revenue x (e / e – 1) and
Marginal Revenue = Average Revenue x (e – 1 / e)
Where, e stands for point elasticity of demand on the average revenue curve. With the help of these formulae, we can find marginal revenue at any point from average revenue at the same point, provided we know the point elasticity of demand on the average revenue curve. Suppose that the price of a product is Rs.8 and the elasticity is 4 at that price. Marginal revenue will be:
M = A (( e – 1) / e)
= 8 (( 4 – 1 / 4)
= 8 x 3 /4
= 24 / 4
Marginal Revenue is Rs. 6.
Suppose that the price of a product is Rs.4 and the elasticity coefficient is 2 then the corresponding MR will be:
M = A ( ( e-1) / e)
= 4 ( ( 2 – 1) / 4)
= 4 x 1 / 4
= 4 / 4
Marginal revenue is Rs. 1
Suppose that the price of commodity is Rs.10 and the elasticity coefficient at that price is 1 MR will be:
M = A ( ( e-1) / e)
=10 ( (1-1) /1)
=10 x 0/1
Whenever elasticity of demand is unity, marginal revenue will be zero, whatever be the price (or AR). It follows from this that if a demand curve shows unitary elasticity throughout its length the corresponding marginal revenue will be zero throughout, that is, the x axis itself will be the marginal revenue curve.
Thus, the higher the elasticity coefficient, the closer is the MR to AR / price. When elasticity coefficient is one for any given price, the corresponding marginal revenue will be zero, marginal revenue is always positive when the elasticity coefficient is greater than one and marginal revenue is always negative when the elasticity coefficient is less than one.
Kinked Demand curve and the corresponding Marginal Revenue curve
We measure quantity on the x axis and price on the Y axis. The demand curve AD has a kink at point B, thus exhibiting two different characteristics. From A to B it is elastic but from B to D it is inelastic. Because the demand is elastic from A to B a very small fall in price causes a very big rise in demand, but to realize the same increase in demand a very big fall in price is required as the demand curve assumes inelastic shape after point B. The corresponding marginal revenue curve initially falls smoothly, though at a greater rate. In the diagram there is a gap in MR between output 300 and 350.
Generally an Oligopolist who faces a kinked demand curve will make a good gain when he reduces the price a little before the kink (point B), but if he lowers the price below B; the rival firms will lower their prices too; accordingly the price cutting firm will not be able to increase its sales correspondingly or may not be able to increase its sales at all. As a result, the demand curve of price cutting firm below B is more inelastic. The corresponding MR curve is not smooth but has a gap or discontinuity between G and L. In certain cases, the kinked demand curve may show a high elasticity in the lower portion of the demand curve beyond the kink and low elasticity in higher portion of the demand curve before the kink Marginal revenue to such a demand curve will show a gap but instead of at a lower level, it will start at a higher level.
Relationship between AR, MR, TR and Elasticity of Demand
In the diagram AR is the average revenue curve, MR is the marginal revenue curve and OD is the total revenue curve. At the middle point C of average revenue curve elasticity is equal to one. On its lower half it is less than one and on the upper half it is greater than one. MR corresponding to the middle point C of the AR curve is zero. This is shown by the fact that MR curve cuts the x axis at Q which corresponds to the point C on the AR curve. If the quantity is greater than OQ it will correspond to that portion of the AR curve where e<1 marginal revenue is negative because MR goes below the x axis. Likewise for a quantity less than OQ, e>1 and the marginal revenue is positive. This means that if quantity greater than OQ is sold, the total revenue will be diminishing and for a quantity less than OQ the total revenue TR will be increasing. Thus the total revenue TR will be maximum at the point H where elasticity is equal to one and marginal revenue is zero.
Significance of Revenue curves
The relationship between price elasticity of demand and total revenue is important because every firm has to decide whether to increase or decrease the price depending on the price elasticity of demand of the product. If the price elasticity of demand for his product is relatively elastic it will be advantageous to reduce price as it increases his total revenue. On the other hand, if the price elasticity of demand for his product is relatively inelastic he should raise the price as it increases his total revenue.
Average revenue, which is the price per unit, considered along with average cost will show to the firm whether it is profitable to produce and sell. If average revenue is greater than average cost, the firm is getting excess profit; if it is less than average cost, the firm is running at a loss.
Firm’s profit is maximum at a point where Marginal revenue is equal to Marginal cost. Any increase in output beyond that point will mean loss on additional units produced; restriction of output before that point will mean lower profit. Thus the concept of average revenue is relevant to find out whether the firm is running on profit or loss; the concept of marginal revenue together with marginal cost will show profit maximizing output for the firm.