Question

In: Economics

Suppose the market for corn in Banana Republic is competitive. The market demand function for corn is Qd = 10 − 0.5P and the market supply function is Qs = P − 2, both measured in billions of bushels per year.

Suppose the market for corn in Banana Republic is competitive. The market demand function for corn is Qd = 10 − 0.5P and the market supply function is Qs = P − 2, both measured in billions of bushels per year.

    1. (a) Calculate the equilibrium price and quantity.

    2. (b) At the equilibrium at part (1a), what is the consumer surplus? producer sur- plus? dead weight loss? Show all of those numerically and graphically.

    3. (c) Suppose the government imposes an specific tax of $6 per unit to raise govern- ment tax revenue. Analyze the problem by shifting the demand curve. What will the new equilibrium quantity be? What price will buyers pay? What price will sellers receive? Show all of those numerically and graphically. Calculate the consumer surplus, producer surplus, government tax revenue and DWL.

    4. (d) Suppose the government imposes a price floor of $10 per bushel.What will the new equilibrium quantity be? What is consumer surplus? producer surplus? dead weight loss? Show all of these numerically and graphically.

    5. (e) Suppose the government imposes a price ceiling of $6 per bushel.What will the new equilibrium quantity be? What is consumer surplus? producer surplus? dead weight loss? Show all of these numerically and graphically.

Solutions

Expert Solution

a. Equilibrium occurs where Demand equals supply.

10-0.5P=P-2

12= 1.5P

Equilibrium Price P*=$8

Equilibrium quantity Q*= 6

b. Consumer surplus= 0.5(20-8)6=$36

Producer surplus=0.5(8-2)6= $18

Deadweight loss=$0

c. Tax on consumer= $6

New demand Qd'=10-0.5(P+6)= 10-0.5P-3= 7-0.5P

New Equilibrium

7-0.5P=P-2

P=9/1.5=6

Price received by producer=$6

Equilibrium Quantity= 6-2=4

Price paid by consumers= $6+$6=$12

Consumer surplus=0.5(20-12)*4= $16

Producer surplus=0.5(6-2)4= $8

Government revenue=$6*4=$24

Deadweight loss=0.5*6*(6-4)= $6

d. Price floor=$10

Qd=10-0.5*10= 5

New Equilibrium quantity=5

Consumer surplus=0.5*(20-10)*5= $25

Producer surplus=0.5(7-2)5+(10-7)*5= $12.5+$25=$37.5

Deadweight loss=0.5(10-7)(6-5)= $1.5

e.

Price Ceiling=$6

Qs=6-2=4

New Equilibrium quantity=4

Consumer surplus=0.5*(20-12)*4+(12-6)*4= $16+$24=$40

Producer surplus=0.5(6-2)*4= $8

Deadweight loss=0.5(12-6)(6-4)= $6

Rahul Sunny answered 2 years ago
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