Question

The demand for DVDs is P = 60 – 0.05Q and the supply is P = 0.025Q. For each of the following scenarios calculate: i) price paid by buyers, ii) price received by sellers, iii) quantity supplied, iv) quantity demanded, v) quantity traded, vi) consumer surplus, vii) producer surplus, viii) tax revenue, ix) deadweight loss. Include a detailed and well-labeled graph with each scenario. Also include a list of which group(s) (either Consumers, Producers, or Government) are most likely to be in favor of each scenario.

            Scenario A: An unregulated market (no price ceilings, price floors, subsidies, or taxes)

            Scenario B: A market with a price ceiling of $15.

            Scenario C: A market with a price floor of $30.

            Scenario D: A market with a $15 per unit tax.

Answer 1

a).

Consider the given problem here the demand for “DVD” is given by, “P = 60 – 0.05Q” and the supply of “DVD” is given by, “P = 0.025*Q”. So, at equilibrium “demand” must be equal to “supply”.

=> 60 – 0.05*Q = 0.025*Q, => 0.075*Q = 60, => Q = 60/0.075 = 800. So, the equilibrium “P” is “P = 0.025*800”, => P = 20.

So, in unregulated market the “P=20” and “Q=800”. So, here “Price paid by buyer” and “piece receive by seller” are same and “Quantity demanded”, “quantity supplied” and “quantity traded” is “800”.

Consider the following fig.

So, here the CS is given by the region “A” and “B” be the PS.

So, “CS = 0.5*800*(60-20)=16,000 and PS = 0.5*800*20 = 8,000. So , TS = CS + PS = 16,000 + 8,000 = 24,000 and here don’t have any “dead weight lose” and “tax revenue” is also zero.

b).

Now, assume that a price ceiling of “$15” < 20, => it’s a binding price ceiling. So, at this price “Qd=900” and the “Qs=600”, since “Qd > Qs”, => the quantity traded is “Qs=600”. We will get these quantities by just putting “P=15” into the demand and the supply function respectively.

Here also the “price paid by buyer” and “price receive by seller is same” is as “15”. Consider the following fig below.

So, in the fig the “CS” is given by the are “A+B” and the “PS” is given by the are “C”.

=> CS = 0.5*600*(60-30) + 600*(30-15) = 0.5*600*30 + 600*15 = 9000 + 9000 = 18,000.

=> PS = 0.5*15*600 = 4500.

Here “DWL” is given by the are “D”, => 0.5*(800-600)*(30-20) + 0.5*(800-600)*(20-15), because the equilibrium “P” is 20 and “Q” is “800”.

= 0.5*200*[(30-20) + (20-15)], => 0.5*200*10 = 1000. Now, the because there don’t have any “tax”, => don’t have any “tax revenue”.

c).

Now, assume that a price floor of “$30” > 20, => it’s a binding price floor. So, at this price “Qd=600” and the “Qs=900”, since “Qd < Qs”, => the quantity traded is “Qd=600”. We will get these quantities by just putting “P=30” into the demand and the supply function respectively.

Here also the “price paid by buyer” and “price receive by seller is same” is as “30”. Consider the following fig below.

So, in the fig the “CS” is given by the are “A” and the “PS” is given by the are “B + C”.

=> CS = 0.5*600*(60-30) = 0.5*600*30 = 9000.

=> PS = 0.5*15*600 + 600*(30-15) = 4500 + 600*15 = 13,500.

Here “DWL” is given by the are “D”, => 0.5*(800-600)*(30-20) + 0.5*(800-600)*(20-15), because the equilibrium “P” is 20 and “Q” is “800”.

= 0.5*200*[(30-20) + (20-15)], => 0.5*200*10 = 1000. Now, the because there don’t have any “tax”, => don’t have any “tax revenue”.

d).

Now, consider the case of a quantity tax of “$15”. So after the imposition of the tax the new supply curve is given by, “P = 15 + 0.025*Q”. So, the new equilibrium is given by “E1”. So, at the new equilibrium the corresponding piece is “P=30” and the quantity traded is “600” and at that quantity traded the seller will get “P-15)=15.

So, here the “price paid by buyer” is “30”, “price receive by seller” is “15” and the quantity demanded and the quantity supplied and the quantity traded is same as “600”. Consider the following fig below.

So, in the fig the “CS” is given by the are “A” and the “PS” is given by the are “C”.

=> CS = 0.5*600*(60-30) = 0.5*600*30 = 9,000 and PS = 0.5*15*600 = 4,500

Here “DWL” is given by the are “D”, => 0.5*(800-600)*(30-20) + 0.5*(800-600)*(20-15), because the equilibrium “P” is 20 and “Q” is “800”.

= 0.5*200*[(30-20) + (20-15)], => 0.5*200*10 = 1000. Now, here the tax revenue is given by “15*Q" = 15*600 = 9000.