[Note]
See accompanying letter
It is required to find the elasticity of the private demand curve (D 1 ), from which the Marginal Revenue (MR 1 ) curve can be derived, of the first duopolist A. i.e. it is required to find how much extra A must produce to provoke a unit drop in price.
If he produces so much as to produce a unit drop in price, the value of D 2 at the new equilibrium position will be less by 1 unit. Now D 2 - MR 2 depends on the elasticity of D 2 and this depends on market elasticity and the cost elasticity of A. Both these we may take to be unaltered by the increase of A's output and the unit fall in price. Consequently in the new equilibrium MR 2 will be down by 1 unit (D 2 - MR 2 having remained constant). From this it is possible to deduce, by reference to B's cost curve, B's restriction of output.
Then since we know the amount which the market will absorb and the amount by which B will restrict in response to a unit drop in price, we infer how much A must produce in order to provoke a unit drop in price. i.e. we know the elasticity of A's private demand curve.
The essential point of this is that we dont need to know the elasticity of D 2 or the value of MR 2 to determine the elasticity of D 1 . It is sufficient to know the cost gradient of B taking into account the fact that we also know that MR 2 , whatever its value and elasticity, will in fact be down by 1 unit.
One firm produces a substantial proportion of total output. There are no frictions due to imperfections of competition.
Traditional economics has had much difficulty here. (In fact, there nearly always are imperfections of competition due to unhomogeneous products.)
Paradox. That if any one competitor drops his price infinitesimally he can get the whole market, & then they can get it back again & so on. Also the assumptions as to what each thinks the other will do add to the indeterminateness.
But perhaps the paradoxes arise because the theorists always assumed there <was> no cost of production.
But assume there are costs of prod n , & marg. rev = marg costs in equili m , & marg. costs are rising.
We want to determine the demand curve f[or] the individual competitor. (It will certainly have a negative inclination. If we can determine it we can derive the marg. rev. curve.).
Suppose the indiv. competitor is f[or]. some reason out of equil m & is prepared to expand output. We want to know how much extra he can market when price drops Dy.
(a) What is the extra output wh[en]. the mkt. will take at price Dy --(call it Dx)
(b) What will other competitors do?
With finite costs & rising marg. costs they will <restrict> output.
- The orig. competitor can market an extra amount Dx+Dz. [Fig. 1]
Price fall of Dy leads to increased demand of mkt. of Dx. But orig. competitor mkts. more than this by the amt. his competitors can no longer afford to produce owing to drop in price. His dem. curve has a greater elasticity than that o[f] the market. We can then derive a marg rev. curve
For a monopolist, his private demand curve is that of the market. There is a gradual transition to perf. comp. where demand curve is horizontal.
Oligopoly does imply increasing costs.
The analysis won't work for decreasing costs. There is no equilibrium. The other competitors restrict output indefinitely as the first increases output.
If there is a small number of firms & no imperfect competition profits must be supernormal, with falling demand curve & rising cost curves.
There cannot be a small number of firms if there is free entry, because profits wd. then tend to normal.
[Note. March 1934. This whole treatment of duopoly is unsound, as admitted by Harrod after criticism by J.A.L. and O.E.P. Harrod has now worked out a very elegant solution (see elsewhere)] J.A.L. (in LaN, MS 5248/Folder 284 ff. 35-37).
A similar point was raised by W. M. Allen (La Nauze's tutor at Balliol College), in a note on "Duopoly", on which Harrod commented in a letter to Meade on 6 March 1935 (letter 437 ; this letter, however, may be misdated and actually have been written on 6 March 1934: see note 1 to letter 437 ).