TR, AR and MR Curves in Competitive Markets | Economy

In this article we will discuss about the nature of firm’s TR, AR and MR curves in perfectly and imperfectly competitive markets.

The AR and MR Curves in the Imperfectly Competitive Market and their Relation:

If the firm wants to sell more in an imperfectly competitive market, it would have to reduce the price of its product. That is, as q increases, the firm’s average revenue (AR = p) diminishes. Therefore, the firm’s AR curve would be downward sloping to right, i.e., negatively sloped, like the AR curve given in Fig. 3.1. Draw this curve as a straight line for the sake of simplicity.

If the position of the firm’s straight line AR curve, then the position of its MR curve would also be known, i.e., to draw the MR curve. Of course, for this, to know the relation between AR and MR of a firm, as discussed below. Suppose that the equation of the straight line AR (= p) curve is

 

 

 

 

 

 

Since equations (3.12) and (3.14) are both straight lines, it is obvious that if AR curve of the firm (3.12) is a negatively sloped (slope = − b, b > 0) straight line, then the firm’s MR curve (3.14) is also a negatively sloped (slope = − 2b) straight line, and the numerical slope of the MR curve (here 2b) is twice as much as that of the AR curve (here b), i.e., the MR curve would be twice as steep as the AR curve.

Also, from (3.8),

 

 

 

 

we obtain:

as q → 0, MR → p (= AR)

i.e., when the quantity sold is infinitesimally small, AR and MR is obtained  to be (almost) equal to each other. This implies that when q is infinitesimally small, both AR and MR would start from the same point on the vertical axis, and then both would be sloping downward to right, and have just obtained, the numerical slope of the MR curve would be twice as much as that of the AR curve.

This signifies that the straight line MR curve would bisect the perpen­dicular that is dropped from any point on the straight line AR curve upon the vertical axis. When this relation between the AR and MR curves is known, the marginal curve can be easily drawn from the given average revenue (AR) curve as shown in Fig. 3.1.

Here, the AR curve has started from the point A on the vertical axis. So the MR curve would also start from the same point. Again, the MR curve is obtained which would pass through the mid-point K of the perpendicular NP₀ dropped from any point N on the AR curve upon the vertical axis. Therefore, the straight line joining the points A and K is the MR curve (AC) associated with the AR curve AB in Fig. 3.1.

It can also be proved from the above relation between the straight line AR and MR curves in terms of geometry. Suppose that the negatively sloped straight lines AB and AC in Fig. 3.1 are, respectively, the AR and MR curves of a firm.

These two curves would start from the same point (here A) on the vertical axis. Now, at any point, N, on the AR curve, p = OP₀ and q = OQ₀. The perpendiculars NQ₀ and NP₀ have intersected the MR curve at the points S and K, respectively.

 

 

 

 

 

 

 

 

 

Therefore, side NK = side P₀K can be obtained, i.e., K is the mid-point of the perpendicular NP₀. Since the MR curve passes through the point K (by construction), it is established that the perpendicular, NP₀, dropped from any point on the AR curve upon the vertical axis, is bisected by the MR curve.

TR Curve in Imperfectly Competitive Market:

It is know that if the AR curve is a negatively sloped straight line, then the TR curve would be a parabolic curve shaped like an inverted-U, and it would start from the origin. A TR curve in Fig. 3.2(a) is drawn in such a way, and the corresponding straight line AR and MR curves in Fig. 3.2(b).

Under imperfect competition, as the quantity sold in­creases, MR, i.e., the rate of change of TR, diminishes. But, so long as MR is positive, TR increases (at a diminishing rate) as q increases. It follows then that TR may become the maximum only when MR is zero at some q.

For, as q increases further MR becomes negative and TR diminishes. In Fig. 3.2, when q = OQ* and MR = 0, TR becomes the maximum. If q increases beyond OQ*, MR becomes negative and TR diminishes.

TR, AR and MR Curves in the Perfectly Competi­tive Market:

In the perfectly competitive market, the firm can sell more or less any quantity of its product at the price determined in the market. That is why, here, the AR (=p) would be a con­stant, independent of q, and the firm’s AR curve would be a horizontal line as has been shown in Fig. 3.3.

Again, here, since at any q, MR = AR (=p) = constant, the firm’s AR curve itself would be its MR curve. That is, in the perfectly competitive market, the firm’s AR and MR curves would be an identical horizontal straight line, as shown in Fig. 3.3 (b).

Now come to the shape of the total revenue (TR) curve of a firm. From (3.1) TR = p x q = TR (q),  TR = 0 at q = 0 is obtained, i.e., the TR curve will start from the point of origin. Besides, from (3.8)

 

 

 

 

 

 

a positive constant; and it would be equal to the price (constant) of the product. Therefore, the TR curve of a competitive firm would be a positively sloped straight line starting from the origin. A curve in Fig. 3.3 (a) is drawn in such a way,