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The marginal prime cost curve is marginal both to the average total cost curve & to the average prime cost curve, since the difference between total cost & total prime cost is constant.
The "`marginal increment of demand curve"  is marginal to the demand curve.
In your diagram the demand curve cuts the total cost curve at the same output as the corresponding marginal curves cut each other.
But when two average curves cut it is impossible that the marginal curves should cut at the same output. I have been accustomed to work by geometry, but I think the above proposition also follows from your formula-- where M = marginal value, A = average value, e = elasticity of the average curve. 
When the average curves cut the average value is the same on both curves, but the elasticities are different, so that it is impossible for the marginal values to be equal.
Only when the average curves are tangential [b] are both the average values & the elasticities equal, & only then can both the average & the marginal values coincide.
Long period equilibrium in an imperfect market is attained when the "particular demand curve" is a tangent to the long period average cost curve.
I am grateful for your formula . I had come upon the same thing in my geometry, but had not seen it in so neat a form.
2. Harrod, "The Law of Decreasing Costs" ( 1931:2 ), p. 571. The error was also pointed out by Viner: letter 227 , [jump to page] . Harrod corrected the error in his "Decreasing Costs: An Addendum" ( 1932:6 ), p. 492.
3. E. Austin G. Robinson, Joan Robinson's husband.
4. Harrod's name for what was later called "marginal revenue": see "Notes on Monopoly and Quasi-Competition", here as essay 6 , [jump to page] , "Notes on Supply" ( 1930:3 ), pp. 238-39, and "The Law of Decreasing Costs" ( 1931:2 ), p. 571.
5. Harrod, "The Law of Decreasing Costs" ( 1931:2 ), p. 570n.
- a. ALS, two pages on one leaf, plus ANS, two pages on two sheets, in HP IV-1089-1107. Reproduced by kind permission of the Provost and Scholars, King's College, Cambridge.
b. Ms: «tangental».
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