Question

Suppose that demand and supply functions for good X are:

Q_D=90-10P (P=9-0.1Q_D)

Q_S=20P-6 (P=0.3+0.05Q_S)

a. Graph this situation.

b. What is the equilibrium price and quantity in the market for good X?

c. What is consumers surplus? Producers surplus?

d. Suppose the government imposes a per unit tax on good X equal to 1 dollar (per unit). What is the new equilibrium price and quantity? How much revenue would this tax raise for the government? What is consumers surplus? Producers surplus?

e. Suppose that, instead of the tax, the government imposes a price ceiling at $2. What is the new equilibrium price and quantity? Consumers surplus? Producers surplus?

Answer 1

(a) for the graph, we simply need few points of the curve and some information regarding the slope to draw the curve. Following pictures represents the method as well as the graph

(b) equilibrium occurs where quatity of demand is equal to the quantity of supply. So simply equate the equations to find out equilibrium quantity and price. Following pictures are showing working for the same

(c) following picture shows the method to find out consumer and producer surplus by using the diagram. Also reffer to the diagram above to locate the triangles.

(d) now unit tax is imposed, which changes the situation. Following pictures will show the new equilibrium prices and quantity, tax revenue and producer and consumer surplus. Here we found surpluses using integration method. You can use diagram as well.