Question

a) Suppose a tax on beans of $0.2 per can is levied on firms. As a result of the tax, the equilibrium price increases from $0.4 to $0.5. What fraction of the incidence (tax burden) falls on consumers? On firms? Suppose the supply elasticity is 0.4. What must the demand elasticity be? (8 Points)

(b) If the demand function for orange juice is expressed as Q = 1000 − 400p, where Q is quantity in gallons and p is price per gallon measured in dollars. For what values of prices the demand for orange juice inelastic? (7 Points)

(c) Suppose demand and supply for a good is given by QD = 150 − 2P and QS = 50 + 23P. The government imposes a price oor of $3. What is the quantity bought and sold in the market. (7 Points)

(d) Leonardo is indierent between lahmacun and pizza. Lahmacun sells for $2 and pizza sells for $1 per serving. Assuming that Leonardo has a budget of $10. How will he spend it? Explain your answer by drawing Leonardo's budget line and indierence curves.(8 Points)

Answer 1

(a)

Given, tax on beans = 0.2

Because of the tax, the equilibrium price for the consumers increase from 0.4 to 0.5

This indicates that half of the burden of the tax i.e. $0.1 in this case - is borne by the consumers. Thus, the fraction of tax incidence on consumers = 1/2 or 50%

As a rule of thumb, tax incidence depends on the relative price elasticity of supply and demand i.e. when supply is more elastic than demand, consumers bear most of the tax burden. And when demand is more elastic than supply, producers bear most of the cost of the tax. However, when both the demand and supply have the same elasticity, the tax burden is borne equally by the consumers and producers.

Thus, the elasticity of supply = elasticity of demand = 0.4

Ans. Ed = 0.4

(b)

Given, demand equation, Q = 1000 - 400P

The demand for orange juice is said to be inelastic when e<1

where elasticity, E = dQ/dP. P/Q

= - (400). P/Q

For all values of Q, price should lie between 0 and 2.5 such that the elasticity of demand is inelastic.

Ans. 0<P<2.5

(c)

Given, demand Q = 150 - 2P and supply Q = 50 + 23P

In equiibrium, demand = supply

150 - 2P = 50 + 23P

Thus, 100 = 25P or P = 4

In equilibrium, Q = 142 and P = 4

At a binding price floor of P = 3, quantity demand, Q = 144 and quantity supplied, Q = 119

Thus, excess supply in the economy = 25 units

(d)

At a budget of M = $10, Leonardo's budget constraint is given by:

2L + 1P = 10

where L = Lahmacun and P = pizza

Given his budget constraint, Leonardo can spend his $10 on any of the following bundles:

(4,2) (3,4) (2,6) (1,8)

Since Leonardo is indifferent between Lahmacun and Pizza i.e. he derives equal utility from consuming both, hence he will choose the bundle with 1 unit of Lahmacun and 8 units of Pizza, since that maximizes his utility.

Maximum utility = 9 utils

Ans. 1 units of lahmacun and 8 units of pizza