# Ad valorem tax on the consumer Watch

1. Question:
Many studies on rats and mice have established that charred meat grilled over hot coals causes cancer. Since the government cannot easily regulate home cooking methods, it has proposed to place a 100 percent tax at the retail level on charcoal briquets. The daily demand for charcoal was P = 120 - 2Q and the supply was P = 30 + Q, where P is in dollars per bag and Q is the number of bags of charcoal sold weekly.
a) What is the before and after tax price of charcoal?
b) What is the before and after tax quantity of charcoal?
c) How is the tax divided among sellers and buyers?

So I can do the before price and quantity very easily, as equating the 2 equations gives Q=30 which substituted back into them gives P=60.
However the after tax equilibrium is confusing me greatly. I appreciate this is not a flat tax e.g. 4 dollars per bag, but is an ad valorem tax (a percentage of the selling price added on top). Thus I'm unsure on how the equations and so the equilibrium will be affected. I appreciate that the ad valorem tax means that the new price is (1+t)p which in this case will be 2p as opposed to a flat tax price of p+t.

I'm unsure how to represent this in the equation, simply doubling them gives the same quantity but double the price, but surely the quantity will be affected as well? If not then demand is perfectly inelastic?

Any help appreciated on parts b) and c) of the question

Thanks

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Updated: November 27, 2010
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