2. Suppose a market is characterized by the following supply and demand equations:
QD=1,000-5P
QS=-500+10P
A) Determine equilibrium price and quantity.
B) Suppose that the government taxes production such that for every unit produced, sellers must pay the government $10. Determine the new equilibrium price(s) and quantity.
C) Suppose that instead of taxes, the government imposes a price floor such that the minimum amount the good can be sold for is $150. Determine the new equilibrium price and quantity.
D) Determine producer surplus, consumer surplus, and total surplus under parts A), B) and C). Are producers or consumers better off under either form of government intervention? How do you know?
a. At Equilibrium, Qd=Qs
1000-5P= -500+10P
P*= 1500/15=$100
Q*= -500+10*100= 500
b. Tax=$10
New quantity supplied= Qs'=-500+10(P-10)= -600+10P
-600+10P=1000-5P
P**= $466.7
Q**= 106.7
C. Price floor=$150
So, Price=$150
Quantity=1000-5*150= 250
D. Part A:
CS=0.5(200-100)500=$25000
PS=0.5(100-50)500= $12500
TS=$37500
Part B:
CS=0.5(200-106.7)(466.7)=$21771.5
PS=0.5(96.7-50)(466.7)=$10897.4
TS=$32668.9
Part C:
CS=0.5(200-150)250=$6250
PS=(150-75)(250)+(0.5(75-50)250)=$21875
TS=$28125
e. consumers are better off under Taxes.
Producers are better off under price floor.
We know this by comparing consumer and producer surplus
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