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

Qd=10,054-26P+0.01M+1.5Pr where P is the price of widgets, M is income, and Pr is the price of a related (fictional) good, the wodget. Suppy of widgets is determined by: Qs=60P-1000 (a) determine whether widgets are a normal or inferior good, and whether widgets and wodgets are substitues or complements. (b) Assume that M=$56,000 and Pr=$112. Solve algebraically to determine the equlibrium price and quantity of widgets. (c) Generate a supply and 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 Qs=55P-700. Solve algebraically for the new equilibrium price and quantity of widgets after these two changes.