A determine whether widgets are a normal or inferior good

Question

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

Q_D = 1200 - 15P + 0.05M - 10P_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 = 700 + 35P

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

b. Assume that M = $53,000 and P_R = $55.00. 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 rises to $57,000 and supply conditions change such that Q_S = 800 + 45P. Solve algebraically for the new equilibrium price and quantity of widgets after these two changes.