Question

4. (8 marks) The inverse market demand and market supply for whiskey are as follows (P is in dollars per liter and Q is in millions of liters) PD 30 QD pS 2 QS a. Find the equilibrium price and quantity in the whiskey market. b. To discourage consumption of whiskey, the government imposes a per unit tax, t $6 on whiskey. What is the effect of the tax on the equilibrium quantity and price? What percent of the tax is borne by consumers and by producers? c. Draw a demand-supply diagram to show your results in (a) and (b) diagrammatically d. What is the effect of an increase in t on the equilibrium quantity of whiskey in general? Obtain an expression for equilibrium quantity and show how it changes when t changes

Answer 1

4. The demand and supply equation are given be
The demand and supply equation are given be P = 30 - Q or Q = 30 - Q and p = 2Q or Q = 0.5P �The equilibrium quantity would be where the quantity demanded is equal to the quantity supplied, ie where�30 - P = 0.5P or 30 = 1.5P or P* = 20 dollars. The equilibrium quantity would be�Q* = 0.5P* or A* = 0.5 times 20 or A* = 10 units.�If per unit tax would be imposed to the supply as�(P - t) = 2Q or P - 6 = 2Q�or�Q = 0.5P - 3. The equilibrium price would be where�0.5P - 3 = 30 - P�or 1.5P = 33�or�P* = 22�dollars, and equilibrium quantity would be�Q* = 30 - P*�or�Q* = 30 - 22 or�Q* = 8�units. The producers receive�(P* - t) = 16�dollars. As can be seen, the equilibrium price have risen by $2 than
or and or .

(a) The equilibrium quantity would be where the quantity demanded is equal to the quantity supplied, ie where or or dollars. The equilibrium quantity would be or or units.

(b) If per unit tax would be imposed to the supply as or or . The equilibrium price would be where or or dollars, and equilibrium quantity would be or or units. The producers receive dollars. As can be seen, the equilibrium price have risen by $2 than before for the consumers while in terms of producers, price reduced by $4. The equilibrium quantity in the market has decreased by 2 units (10 - 8).

For the $6 tax, the consumers are paying $2 more than before ($22 - $20), while producers are getting $4 less than before ($20 - $16). Hence, the percent of tax borne by consumer is $\frac{2}{6}*100 = 33.33$ percent, while the percent of tax borne by producer is $\frac{4}{6}*100 = 66.67$ percent.

(c) The graph is as below.

The before tax equilibrium is at point E. After the tax is imposed, the equilibrium price (what consumers pay) and quantity shifts corresponding to point A. The producers receive price corresponding to point B. The amount of tax is AB, among which, burden on consumer is AC per unit, and burden on producer is BC per unit.

(d) For the tax be $t, the relevant supply curve would be or . The equilibrium price in the market would be where or or dollars. The equilibrium quantity would be or or units. The producers receive dollars.

For , we have $\frac{\mathrm{d} Q^*}{\mathrm{d} t} = - 1/3$ , which means that as the tax increases by a marginal unit, the equilibrium quantity decreases by -1/3 or -0.33 units.