Suppose the Demand for Some Good Can Be Estimated Using $\frac { d } { ( b + d ) }$

question 58

Essay

Suppose the demand for some good can be estimated using the equation Q_D = a - bP,and the supply can be estimated using the equation Q_S = c + dP,where a is the intercept and b is the slope of the demand curve,and c is the intercept and d is the slope of the supply curve.P is the equilibrium price in the market.
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A)If a per-unit excise tax of size T were imposed on each unit of this good sold in the market,show that the percentage of the tax born by the consumer is $\frac { d } { ( b + d ) }$ ,and the percentage of the tax born by the supplier is $\frac { - b } { ( b + d ) }$ .
[Hint: The tax (T)is equal to the price the consumer pays (i.e. ,P_D)minus the price received by the supplier (P_S).Therefore,T = P_D - P_S.Rearrange and substitute into one of the equations above.]

• A)If a per-unit excise tax of size T were imposed on each unit of this good sold in the market,show that the percentage of the tax born by the consumer is \(\frac { d } { ( b + d ) }\) ,and the percentage of the tax born by the supplier is \(\frac { - b } { ( b + d ) }\) .
• [Hint: The tax (T)is equal to the price the consumer pays (i.e. ,P_D)minus the price received by the supplier (P_S).Therefore,T = P_D - P_S.Rearrange and substitute into one of the equations above.]

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