Question

2. Symbolic analysis of supply and demand: The following demand and supply functions provide a relatively general description of a market: Qs = D + eP where P is the price, Y is a variable denoting income, and Qd and Qs are the quantity demanded and the quantity supplied. The constants A, b, c, D, and e have values greater than zero. (a) Identify the parameters, endogenous variables, and exogenous variables in the above system of equations. (b) Derive expressions for the equilibrium market price (P") and quantity (Q and illustrate your answers with a graph. Be sure to specify the symbolic values of the demand and supply curves where they intersect with the P-axis and Q-axis in the positive quadrant. (c) Given your results from part (b), use calculus to determine the effect of a small change in income on the equilibrium price (P"). Use your answer to confirm that this is a normal good. (d) Now find the same thing as in part (c) using a different approach. Set the expressions for Qd and Qs from equations (3) and (4) equal to each other. This is the market equilibrium condition and thus, in this expression, we can think of the price as the equilibrium price. In equilibrium the price is a function, P (Y), dp* of Y. Differentiate both sides with respect to Y and solve for dy. (e) Find the range of prices, in terms of A, b, c, D, and e, for which the price elasticity of demand is elastic, i.e. ε <-1. Hint: your equation should depend on various parameters and Y.

Answer 1