a)Suppose the quantity of good X demanded by individual 1 and 2 is given

X₁= 10 - 2P_X+ 0.1I₁+ 0.5P_Y

X₂= 17 - P_X+ 0.05I₂+ 0.5P_Y

(i)What is the market demand function to total X (= X₁+ X₂) as a function of P_X, I₁, I₂and P_Y.

(ii)Now given the values of some of the variables as follows: I₁= 40, I₂= 20, P_Y= 4

Give the algebraic equation for the market demand curve for total X.

(b) (i)Calculate the point elasticity of demand from the demand functions

Q = 100 - 2P +¹⁰⁰/_Pat P = 10 and Q = 90

(ii)Given a demand curve which is a rectangular hyperbola and with a functional form Q =¹/_P. Show arithmetically that the point elasticity of demand will be unitary throughout the demand curve.

(iii)Given the demand and supply functions shown below, calculate the equilibrium price and quantity at which the market clears.

Q_d= 90 - 2P

Q_s= P - 3