5. Suppose the demand for a particular wine can be described by the function
$q^P(p_d) = 100 - p_d$
where $p_d$ is the price paid by the consumer.
(a) If a specific (quantity) tax of $t = \$10$ is placed on Wine and this tax is paid by
the consumer find the demand for wine as a function of, $p_s$, the price paid to the
producer. Recall that
$p_d = p_s + t$
You are asked to find
$q^P(p_s)$
(b) If an ad valorem tax of $\tau = 20\%$ is place on Wine and this tax is paid by the
consumer, find the demand for wine as a function of $p_s$, $q^P(p_s)$.
(c) If the supply of the wine is described by the function
$q^S(p_s) = 2p_s - 10$
determine the equilibrium (price and quantity) in the market for the cases of (i)
no tax, (ii) the specific tax $t = \$10$ and (iii) the ad valorem tax $\tau = 20\%$.
(d) For the case of the specific tax $t = \$10$, determine the incidence of the tax and
calculate the deadweight loss of taxation.
(e) For the case of the specific tax $t = \$10$, find price paid by consumer and received
by the firm and the quantity sold when demand is $q^P(p_d) = 100 - p_d$ and the
monopolist has marginal cost $mc = 5 + \frac{1}{2}q$.
