Tax problem - Supply. Demand, and a Tax (Class notes by...

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Supply. Demand, and a Tax (Class notes by E.S. de Dios) How do equilibrium price and quantity change when a tax is imposed? Let the demand and supply functions be given as usual by Q D = a bP (1a) Q S = c + dP (1b) (Here, a , b , c , and d are all arbitrary positive numbers.) Then without a tax, equilibrium price is given (as we all know) by equating Q D and Q S and solving for P . a bP = – c + dP (2) which yields P + = a + c b + d and Q + = a b a + c b + d = ad - bc b + d . (3) How must this change when a tax equal to T per unit is imposed? Remember that sellers react to the price they receive while buyers act on the price they observe. Without a tax, these two prices were the same, namely P . But when there is a tax, the two are different, and we can distinguish P B , the price the buyer pays, and P S , the price the seller receives. The price the buyer pays equals the price the seller receives plus the tax, i.e., P B = P S + T . (4) If the price the buyer pays is the price we observe, then
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Tax problem - Supply. Demand, and a Tax (Class notes by...

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