- Question 5 20 Marks A Function G X Is Strictly Increasing If G X 0 On Its Domain Assume The Supply And Demand Fu 1 (125.34 KiB) Viewed 30 times
g 0 (x) > 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 0 (P) > 0 on its domain, and that ∂ ∂Z D(Z, Y
) < 0, and ∂ ∂Y D(Z, Y ) > 0, 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 P is 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 P
is a function of T. Is price (P) an increasing or decreasing
function of tax (T)? Show your working steps to support your
answer.
Question 5 (20 marks) A function g(x) is strictly increasing if g'(x) > 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 a „D(Z,Y)< 0, and <D(Z,Y) > 0, az ay 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 P is 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 P is a function of T. Is price (P) an increasing or decreasing function of tax (T)? Show your working steps to support your answer.