Answer to Question #19542 in Differential Equations for Ashley

Question

1. Qd = kP−e(e > 0)
Qs = c(P − T0)
are the demand and supply curves for a commodity whose price is P.
T0 is a sales tax imposed by the government on sales of this commodity.
(a) Compute the price elasticity of demand and the price elasticity of supply of this commodity.
(b) Find an expression for ∂P/∂T0 where P is the equilibrium price in this market.
(c) Show that 0 < ∂P/∂T0 < 1.
(d) Total tax revenue collected by the government is R = T0Q. Find an expression for ∂R/∂T0.