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

Q_D = 13,000 - 270P + 0.0001M + 0.5P_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 = 350P - 5

1. Determine whether widgets are a normal or inferior good, and whether widgets and wodgets are substitutes or complements.
2. Assume that M = $55,000 and P_R = $19.00. Solve algebraically to determine the equilibrium price and quantity of widgets.
3. 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?
4. Now assume two events occur: demand changes such that the intercept in the demand equation rises to 13,005 and supply conditions change such that

Q_S = 390P + 150. Solve algebraically for the new equilibrium price and quantity of widgets after these two changes.