The following represents demand for widgets: QD = 680 – 9P +0.006M – 4PR, where P is the price of widgets, M is income, and PR is the price of a related good, the wodget. Supply of widgets is determined by QS = 30 + 3P. a) Determine whether widgets are a normal or inferior good, and whether widgets and wodgets are substitutes or complements. b) Assume that in 2010 M = $15,000 and PR = $20. Solve algebraically to determine the 2010 equilibrium price and quantity of widgets. c) Generate a 2010 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 drops to $13,000 and supply conditions change such that QS = 50 + 3P. Solve algebraically for the new equilibrium price and quantity of widgets after these two changes. (When you’re typing your answers, you can sub- or superscript by right-clicking and selecting Font. If you want to get really fancy, you can use the Equation Editor which may already be in the Insert tab, or you can hit the office button, select Word Options and find it in the Customize screen.)