1. The following represents demand for widgets (a fictional product):

Q_D = 10,054 - 26P + 0.01M + 1.5P_R

where P is the price of widgets, M is income, and P_R is the price of a related (fictional) good, the wodget. Supply of widgets is determined by

Q_S = 60P - 1,000

a. Determine whether widgets are a normal or inferior good, and whether widgets and wodgets are substitutes or complements.

b. Assume that M = $56,000 and P_R = $112. Solve algebraically to determine the equilibrium price and quantity of widgets.

c. Generate a supply/demand graph in Excel. Be sure that P is the vertical axis and Q the horizontal. Does the graphical equilibrium correspond to your algebraic equilibrium?

d. Now assume two events occur: income changes such that M = $58,000 and supply conditions change such that Q_S = 55P - 700. Solve algebraically for the new equilibrium price and quantity of widgets after these two changes.