the inverse 7.4.2 The inverse demand function for a good is p = 3 – x², where p is price, x is quantity and p and r are restricted to be non-negative. Show that this is a mono- tonic function and find the ordinary demand function for the good. Also find an expression for the elasticity of demand. %3D - 7.4.3 The demand function for a good supplied by a monopolist is 1000 – p (0 < p< 10). p3 Find the inverse demand function and derive an expression for marginal revenue.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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Question
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Can get help solving 7.4.2 and 7.2.3
METHODS OF DIFFERENTIATION
134
7.4.1 For those functions of Exercise 7.3.1 which are monotonic and differentiable. use
the inverse function rule to find the derivative of the inverse function.
Exercises
7.4.2 The inverse demand function for a g0ood is p = 3 – x², where p is price, x is
quantity and p and a are restricted to be non-negative. Show that this is a mono-
tonic function and find the ordinary demand function for the good. Also find an
expression for the elasticity of demand.
7.4.3 The demand function for a good supplied by a monopolist is
1000 –
(0 <p< 10).
Find the inverse demand function and derive an expression for marginal revenue.
Problems on Chapter 7
7-1. Suppose that a firm's output Q is related to capital input K and labour input L
by the production function
Q = K!/²L!/3
Suppose further that K and L are given by the linear functions
K = 5+ 2t,
L = 2+t.
Find dQ/dt.
7-2 (G) Sometimes relations which are nột given in the form y = f(x) can be put in
%3D
that form by means of simple algebra. Show that the relatioD
1/2,,1/3
= c (x,y > 0)
(7.6)
Jwhere c is a nositive constant, can be put in the form 21
Transcribed Image Text:METHODS OF DIFFERENTIATION 134 7.4.1 For those functions of Exercise 7.3.1 which are monotonic and differentiable. use the inverse function rule to find the derivative of the inverse function. Exercises 7.4.2 The inverse demand function for a g0ood is p = 3 – x², where p is price, x is quantity and p and a are restricted to be non-negative. Show that this is a mono- tonic function and find the ordinary demand function for the good. Also find an expression for the elasticity of demand. 7.4.3 The demand function for a good supplied by a monopolist is 1000 – (0 <p< 10). Find the inverse demand function and derive an expression for marginal revenue. Problems on Chapter 7 7-1. Suppose that a firm's output Q is related to capital input K and labour input L by the production function Q = K!/²L!/3 Suppose further that K and L are given by the linear functions K = 5+ 2t, L = 2+t. Find dQ/dt. 7-2 (G) Sometimes relations which are nột given in the form y = f(x) can be put in %3D that form by means of simple algebra. Show that the relatioD 1/2,,1/3 = c (x,y > 0) (7.6) Jwhere c is a nositive constant, can be put in the form 21
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