See accompanying letter
Let x = be output
p = (average) price
z = marginal cost
k = profit per unit
h = elasticity of demand = .
Then average cost .
In response to small changes in h, the rate of change in profit, k is > the rate of change in price, p if . Now
Now if marginal cost > average cost 1 , is positive [c] = say. So that . if is positive
i.e. if is negative
i.e. if elasticity of demand falls as output rises.
This gives the following general result for a small change in the elasticity of demand
(1) with rising marginal costs--
"The rate of change in profits per unit is greater than the rate of change in price only if elasticity falls as output increases" --if is negative
(2) with constant marginal costs.
whatever be the relation between x and h. However, obviously , which is as in your example on top of p. 86.
(3) with falling marginal costs, if is negative, , but, under certain conditions may be > , so that even in this case the proportionate change in profit may be greater than the proportionate change in prices.
- a. ALS, one page, in HP IV-962. The annexe AD, two pages on one leaf, is in file HP IV-961.
b. Ms: «is».
c. Ms: «+ve».
d. Ms: «+ve».
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