4. (a) Profit-maximizing price must equal p = S MC, where e is the price elasticity of demand. What are the requirements for this condition to hold? In other words, explain both the necessary and sufficient conditions and the requirement related to e. (b) Show that for an elastic demand, by lowering the price profits may go up or down; for an inelastic demand loweing the price must lower the profits. What happens when the elasticity is 1 and price is lowered or raised?

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4. (a) Profit-maximizing price must equal p = S MC, where e is the price
elasticity of demand. What are the requirements for this condition to hold?
In other words, explain both the necessary and sufficient conditions and the
requirement related to e.
(b) Show that for an elastic demand, by lowering the price profits may go
up or down; for an inelastic demand loweing the price must lower the profits.
What happens when the elasticity is 1 and price is lowered or raised?
(c) Show that for a linear demand, p = a – bQ, the elasticity is changing
from o to 0 as price decreases (quantity increases) but the slope is constant;
but for the demand function Q = 100/P, the elasticity is constant but the slope
is changing.
Transcribed Image Text:4. (a) Profit-maximizing price must equal p = S MC, where e is the price elasticity of demand. What are the requirements for this condition to hold? In other words, explain both the necessary and sufficient conditions and the requirement related to e. (b) Show that for an elastic demand, by lowering the price profits may go up or down; for an inelastic demand loweing the price must lower the profits. What happens when the elasticity is 1 and price is lowered or raised? (c) Show that for a linear demand, p = a – bQ, the elasticity is changing from o to 0 as price decreases (quantity increases) but the slope is constant; but for the demand function Q = 100/P, the elasticity is constant but the slope is changing.
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