Consider the demand function:where q = quantity, p = pricea)b)c)d)Q = 2p²60p + 700nFind Total Revenue as a function of p.(Hint: Do not attempt to find Total Revenue as a function of q, as todo so requires use of the inverse demand function which is difficult tofind in this case.Show that when 6p² - 120p + 700 = 0, Total Revenue is at itsmaximum.Find the price and quantity that maximise Total Revenue.Show that the demand elasticity, as a function of p, is given by:ED= (4p²-60p)/(2p²-60p + 700)Show that when demand has unit elasticity (that is, Eª = -1or | Ed = 1), Total Revenue is at its maximum.For what values of p is demand (i) elastic; (ii) inelastic? What is theeffect of a small price reduction on Total Revenue, when demand is(i) elastic; (ii) inelastic?e) Sketch the graphs of the Demand function, Total Revenue andMarginal Revenue as functions of p.Explain, using words and diagrams only, the relationship betweenMarginal Revenue and the Elasticity of Demand.

Total revenue is the total amount of money a business receives from selling its products or…

Answered: Find Total Revenue as a function of p.…

Find Total Revenue as a function of p. (Hint: Do not attempt to find Total Revenue as a function of q, as to do so requires use of the inverse demand function which is difficult to find in this case.

ECON MICRO

5th Edition

ISBN:9781337000536

Author:William A. McEachern

Publisher:William A. McEachern

Chapter5: Elasticity Of Demand And Supply

Section: Chapter Questions

Problem 1.1P: (Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of...

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Question

Consider the demand function:
where q = quantity, p = price
a)
b)
c)
d)
Q = 2p²60p + 700
n
Find Total Revenue as a function of p.
(Hint: Do not attempt to find Total Revenue as a function of q, as to
do so requires use of the inverse demand function which is difficult to
find in this case.
Show that when 6p² - 120p + 700 = 0, Total Revenue is at its
maximum.
Find the price and quantity that maximise Total Revenue.
Show that the demand elasticity, as a function of p, is given by:
ED= (4p²-60p)/(2p²-60p + 700)
Show that when demand has unit elasticity (that is, Eª = -1
or | Ed = 1), Total Revenue is at its maximum.
For what values of p is demand (i) elastic; (ii) inelastic? What is the
effect of a small price reduction on Total Revenue, when demand is
(i) elastic; (ii) inelastic?
e) Sketch the graphs of the Demand function, Total Revenue and
Marginal Revenue as functions of p.
Explain, using words and diagrams only, the relationship between
Marginal Revenue and the Elasticity of Demand.

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Step 1: Introduce the concept of total revenue.

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Step 2: Part (a) Find total revenue as function of p.

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Step 3: Part (b) Find the price and quantity that maximise Total Revenue.

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Step 4: Part (c) Calculate price elasticity.

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