Question 1201755: A local coffee shop charges €2.50 for an espresso. The owner of the coffee shop wants to increase his total revenue. A recent market research shows that the price elasticity of demand for espresso is about 1.80. Should the coffee shop lower or raise the price of espresso? Explain your answer.
b) “The closer the substitute for a good or service, the more inelastic is the demand for it.” Is this statement true or false? Explain your answer
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
A local coffee shop charges €2.50 for an espresso.
The owner of the coffee shop wants to increase his total revenue.
A recent market research shows that the price elasticity of demand for espresso is about 1.80.
Should the coffee shop lower or raise the price of espresso? Explain your answer.
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DEFINITION
Price elasticity of demand is a measurement of the change
in the consumption of a product in relation to a change in its price.
Thus in this problem  = 1.8. (1)
It means, if to follow to the problem LITERALLY, that the dependence Q(consumption)
of P(price) has the form Q = 1.8*(P-2.50).
But it is clear that it is ILLOGICAL: according to (1), if the price rises over €2.50,
the consumption should increase.
So, actually it should be Q = -1.8*(P-2.50),
and my first inference that the "problem's composer" is not able to formulate his "economics problem" correctly.
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Next, I will not consider a profit (since I have no data for calculating it),
and will consider the REVENUE, only. The revenue is
R = P*Q = -1.8*P*(P-2.50), (2)
and our goal (the goal of the coffee shop, from the context) is to increase the revenue (2).
We write the revenue (2) in equivalent form
R = -1.8*P^2 + 1.8*2.50*P.
The derivative  is -2*1.8P + 1.8*2.50, and at the price P= 2.50€ it is
= -2*1.8*2.50 + 1.8*2.50 = -4.5.
Since this derivative is negative, then, if the coffee shop wants to increase the revenue, it should decrease the price from €2.50.
Solved, with complete explanations.
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I answered question "a" ONLY,
and my advise to the visitor is NEVER pack more than one problem/question per post,
in accordance with the rules of this forum (and in accordance with the rules of common sense, too).
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