The supply and demand functions for a generic brand of ink cartridge sold at sta

Question

The supply and demand functions for a generic brand of ink cartridge sold at staples are related by the equations
D: q=-6p+80 S: q=9p-40
where p represents the price in dollars for each ink cartridge and q represents the quantity of ink cartridges sold per day
a) determine the market equilibrium price and quantity
b) if customers are charged a 15% tax, determine the new demand function that relates q, the numberof ink cartridge demanded, to p, the before-tax price per cartridge
c)what would be the new demand function that relates q, the number of ink cartridges demanded, to p, the before-tax price per cartridge if in addition to the 15% tax, the government levied a recycling fee of $1.00 before tax per ink cartridge?
d) what would be the new market equilibrium price and quantity if in addition to the 15% tax the government levied a recycling fee of $1.00 after tax per ink cartridge?

Explanation / Answer

a. market equilibrium occurs when D =S -6p + 80 = 9p -40 120 = 15p p = $8 sub p = 8 into either equations: q = - 6p + 80 = 80 - 6*8 = 80 -48 = 32 catridges b. New demand function Q' = 0.85(-6p)+80 = 80 -5.1p (0.85 is use to calculate after tax) c. New demand function Q'' = 80 - 5.1p - 1 = 79 - 5.1p (the levy is not proportional, so deduct) d. redo the simultaneous equations: 79-5.1p = 9p - 40 (the tax is on the customers, so the supply function is not affected) 119 = 14.1p p = 119/14.1 = $8.44 to the nearest cent sub in either functions: Q = 9(119/14.1) - 40 = 35.95 or 36 since you can't have a 95% of a cartridge

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