Question

Demand and supply in the market for cases of soda pop is given by

Qd=300−11P

and

Qs=4P.

Complete parts a through f below.

​a) What are equilibrium price and​ quantity?

The equilibrium price is

P=​$2020

and the equilibrium quantity is

Q=8080.

​(Simplify your answers. Type integers or​ decimals.)

​b) Suppose the government is concerned about too much sugar in​ peoples' diets and decides to tax soda pop sellers

​$3

per case. What is the equation of the new supply​ curve? Let

Pc

be the price paid by the consumer.

Qs=Pc+

​(Simplify your answers. Type integers or​ decimals.)

​c) What is the​ new, after-tax​ equilibrium?

The​ after-tax equilibrium price is

​$nothing

and the quantity is

nothing.

​(Simplify your answers. Type integers or​ decimals.)

​d) How much do consumers now pay and how much do sellers end up​ receiving?

Consumers will now pay

​$nothing

and firms will receive

​$nothing.

​(Simplify your answers. Type integers or​ decimals.)

​e) What is the value of producer surplus both before and after the tax was​ levied? HINT: Draw it.

The value of producer surplus before the tax was levied is

​$nothing.

​(Round to the nearest cent as​ needed.)

The value of producer surplus after the tax was levied is

​$nothing.

​(Round to the nearest cent as​ needed.)

​f) What is the deadweight loss due to the​ tax? HINT: Draw it.

The deadweight loss is

​$nothing.

​(Round to the nearest cent as​ needed.)

Enter your answer in each of the answer boxes.

Answer 1

a) Qd=300−11P and  Qs=4P are given. These are the demand and supply equations respectively.

Equilibrium price and quantity are calculated by equating the above demand and supply equations i.e.

  Qd =  Qs

300-11P = 4P

300 = 15P

Therefore, P= $20. From this we can calculate the equilibrium quantity from either of the two equations i.e.

Qd=300−11P or Qs=4P. This gives the equilibrium quantity equal to 80 units (=4*20 units).

b) If the government imposes a tax of $3 on soda pop sellers, the supply curve becomes

   Qs = 4(P-3)

It happens because at the new equilbrium price after tax ,the sellers would receive a price which will be less than the equlibrium price by $3 (as $3 is the tax imposed on each unit of soda and goes to the government as tax revenue).

c) New after tax equilibrium is achieved by equating the demand equation with the supply equation (after tax) calculated in part b. So, we have

Qd =  Qs

300-11P = 4P-12

312 = 15P

therefore, P= $20.8 and Q = 4(20.8-3) = 4*17.8 = 71.2 units or 71 units. Hence, the new equilbrium price (after tax) is equal to $20.8 and the new equilibrium quantity (after tax) is equal to 71 units.

d) When a tax is imposed, prices faced by the consumers and producers/ sellers are different. These prices for the above question are $20.8 and $17.8 for consumers and sellers respectively. The consumers pay the equilibrium price after tax but the sellers recieve the price less than the equilibrium price by $3. This happens because $3 per unit of the good is the amount of tax and makes up the government tax revenue, as mentioned earlier.