2. The following demand and supply functions provide a relatively general description of a market: Qd =A BP (3)

Qs = CW + D + EP (4)

where P is the price, W is a variable denoting weather, and Qd and Qs are the quantity demanded and the quantity supplied. A, B, D, and E all have values greater than zero.

(a) There is a third equation (in addition to equations 3 & 4) that completes our mathematical model of market equilibrium. What is it?

(b) Identify the parameters, endogenous variables, and exogenous variables in the above system of equations.

(c) 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.

(d) Given your results from part (a), use calculus to determine the effect of a small change in weather on the equilibrium price (P*). Despite the fact that you don't know how W represents the weather (Temperature? Rainfall? Or something else) can you determine the sign of the expression you find? If so, determine the sign. If not, identify the value of components you can and explain what is ambiguously signed and how its sign would impact your result's value