Question

5. Consider a demand and supply problem where supply of a single good is (s(P) where P is the price of the good, and the demand of the good is Qo(P,Y) where Y is the income of a consumer. The excess demand function is defined as ED(P,Y) = Q(P,Y) – Qs(P). Suppose all (partial) derivatives of demand, supply and ED are continuous and differentiable, and < 0 (demand curve is negatively sloped), D > 0 (i.e. this good is a normal good), > 0 (supply curve is upward sloping). The equilibrium price P*, which depends on the income level of a consumer, is therefore defined by ED(P,Y) = 0. If the income Y increases, do we have a higher or a lower equilibrium price?

Answer 1

For equilibrium, ED(P,Y) = 0

or, Q_D(P,Y) - Q_S(P) = 0

or, Q_D(P,Y) = Q_S(P) is the equilibrium condition.

If Y increases (where, $\partial$Q_D/$\partial$Y > 0), equilibrium price and quantity must rise. This is because AD curve shifts to the right and thereby, intersecting supply curve at a point having higher price level and output level (quantity).