Question

The demand and supply for soft drinks are

given by Q = 10-P and Q = 2+2P, respectively. Suppose now the government imposes a per unit subsidy of $1.5 on the sellers.

a)what is the price received by the sellers after the subsidy has been imposed?

Answer 1

We first rewrite the demand and supply equations as, $P=10-Q$ and $P={Q-2\over2}$ respectively. With $\$1.5$ tax on sellers, the supply curve after tax is $P={Q-2\over2}+{1.5}={Q+1\over2}$.

The new equilibrium quantity can be found by equating $P={Q+1\over2}$and $P=10-Q$. So, ${Q+1\over2}=10-Q$. This gives the new equilibrium quantity as, $Q_T={19\over3}$.

The price sellers receive can now be obtained from the pre-tax supply equation as,

$P={Q_T-2\over2}={{19\over3}-2\over2}=2.17$

Therefore, the price received by the sellers after the subsidy has been imposed is 2.17.