Assume that the demand for iron (the primary component of steel) is Q = P^(-a)? , where the exogenous parameter a>0 takes some fixed value. For all parts assume that the iron market is in equilibrium. You should simplify your answers as much as possible.
(a) Find the inverse demand curve for iron.
(b) Does the demand for iron satisfy the Law of Demand?
(c) What is the elasticity of demand for iron, as a function of Q and the parameter a? For parts (d)-(f) assume that a=2 and the supply of iron is Q = 8P.
(d) What are the equilibrium price and quantity of iron? If the value of a is unknown, then what are the equilibrium price and quantity as functions of a?
(e) Draw a picture that shows the supply and demand curves (including two exact points on each curve) and the equilibrium.
(f) Suppose that increases from its initial value of a=2. Does this represent an increase or decrease in: demand; supply; quantity supplied; and quantity demanded?
For parts (g) and (h) continue to assume that a=2, but now assume that supply increases to Q = 9P.
(g) Find the new equilibrium price and quantity. Draw a new picture, showing the old (assuming Q=8P) and the new demand and supply curves and equilibria. Label the old equilibrium “A” and the new equilibrium “B”.
(h) Going from equilibrium A to equilibrium B, what is the percentage change in price and what is the percentage change in quantity? Are these answers consistent with the elasticity of demand that you computed in part (c)? If not, then why not?