Question

8. Suppose the demand and supply are described by the following equations: D(p)=500-50p and S(p)=-100+50p.

8a. What are the equilibrium price and quantity?

8b. Draw a graph showing consumer and producer surplus when a market is in equilibrium. Label them C and P respectively

8c. Draw a graph to show the effect of a $4 per-unit tax on suppliers:

8d. What are the equilibrium price and quantity after the tax

8e. What are consumer and producer surplus when the market is in equilibrium after the tax? Label C and P.

8f. What is total revenue collected after the tax is implemented? Label it T on the Graph.

8g. Contrast your answer of b to that of e and f. What is the implication from this analysis?

Answer 1

8. Suppose the demand and supply are described by the following equations: D(p)=500-50p and S(p)=-100+50p.

8a. What are the equilibrium price and quantity?

D(P) = S(P)

500-50p = 100+50p

400=100p

p=4 and q=300

8b. Draw a graph showing consumer and producer surplus when a market is in equilibrium. Label them C and P respectively

Graph is shown below

8c. Draw a graph to show the effect of a $4 per-unit tax on suppliers:

The graph in part b shows the effect of a tax by shifting the supply curve up by $4.

8d. What are the equilibrium price and quantity after the tax

Price paid by buyers = 6. Price recevied by sellers = 2. Quantity sold falls to 200

D(P) = S(P) + tax

500-50p = 100+50(p-4)

500-50p = 100+50p-200

600=100p

p=6 and q=200

8e. What are consumer and producer surplus when the market is in equilibrium after the tax? Label C and P.

CS = 0.5*(10 - 6)*200 = $400. PS = 0.5*(200 + 100)*2 = $300

8f. What is total revenue collected after the tax is implemented? Label it T on the Graph.

Total revenue = tax x quantity = 4*200 = 800

8g. Contrast your answer of b to that of e and f. What is the implication from this analysis?

There is a deadweight loss because loss to consumer surplus and producer surplus is not compensated by government revenue