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A function g(z) is strictly increasing if g'(z) > 0 on its domain. Assume the supply and demand functions for a high-tech product are Qs = S(P), QD = D(P+T,Y), where Y is the income, T is the consumption tax on the product, and P is the price. We don't specify a particular analytical form of the supply and demand functions, but we assume that both functions are well defined on their domains and their derivatives exist. We also assume that S'(P) > 0 on its domain, and that

A function g(z) is strictly increasing if g'(z) > 0 on its domain. Assume the supply and demand functions for a high-tech product are Qs = S(P), QD = D(P+T,Y), where Y is the income, T is the consumption tax on the product, and P is the price. We don't specify a particular analytical form of the supply and demand functions, but we assume that both functions are well defined on their domains and their derivatives exist. We also assume that S'(P) > 0 on its domain, and that

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 5 A function g(z) is strictly increasing if g'(z) > 0 on its domain. Assume the supply and demand functions for a high-tech product are Qs = S(P), Qp = D(P +T,Y), %3D where Y is the income, T is the consumption tax on the product, and P is the price. We don't specify a particular analytical form of the supply and demand functions, but we assume that both functions are well defined on their domains and their derivatives exist. We also assume that S'(P) > 0 on its domain, and that D(Z,Y) > 0, D(Z,Y) < 0, and az where Z = P+T. Assume an equilibrium state exists in the sense that the supply and demand are balanced: S(P) – D(P +T,Y) = 0. (1) Assume Pis a function of Y. Is price (P) an increasing or decreasing function of income (Y)? Show your working steps to support your answer. (2) Assume Pis a function of T. Is price (P) an increasing or decreasing function of tax (T)? Show your working steps to support your answer.
Transcribed Image Text:Question 5 A function g(z) is strictly increasing if g'(z) > 0 on its domain. Assume the supply and demand functions for a high-tech product are Qs = S(P), Qp = D(P +T,Y), %3D where Y is the income, T is the consumption tax on the product, and P is the price. We don't specify a particular analytical form of the supply and demand functions, but we assume that both functions are well defined on their domains and their derivatives exist. We also assume that S'(P) > 0 on its domain, and that D(Z,Y) > 0, D(Z,Y) < 0, and az where Z = P+T. Assume an equilibrium state exists in the sense that the supply and demand are balanced: S(P) – D(P +T,Y) = 0. (1) Assume Pis a function of Y. Is price (P) an increasing or decreasing function of income (Y)? Show your working steps to support your answer. (2) Assume Pis a function of T. Is price (P) an increasing or decreasing function of tax (T)? Show your working steps to support your answer.
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