ECON 411 – Find the initial equilibrium values of quantity and price

ECON 411  – Find the initial equilibrium values of quantity and price in the absence of any tax

Subject: Economics    / General Economics
Question
Homework #4
(Econ 411)
Spring 2017 1. Prove that if preferences are ‘Leontie¤’, excess burden is zero.
2. Discuss what di¤erence it may make to workers and their employers if the
50-50 division of social security contributions in the U.S. is changed to
80% by the workers and 20% by the employers.
3. In the diagram below, indicate (do not distinguish between ordinary and
compensated demand):After-tax consumer’s price, after-tax producer’s price, after-tax equilibrium quantity, tax revenue, tax incidence on consumers, loss of consumer surplus, tax incidence on producers, and excess
burden.

4. The equations for the demand and supply of a particular good are respectively given by:
qd = 20 qs = 3ps 2pc Do not distinguish between ordinary and compensated demand in answering these questions.
(a) Find the initial equilibrium values of quantity and price in the absence of any tax.
(b) Assuming a unit tax of 2.5 is levied on this commodity, …nd the new
equilibrium values of quantity and ‘price’.
(c) Find the tax revenues.
1 (d) Find the excess burden.
(e) Find the incidence of the tax on consumers.
(f) Find the incidence of the tax on producers.
(g) Who is e¤ectively paying the tax here and to what degree?
(h) Whom the tax is levied on in this question and what is the signi…cance
of it?
(i) Repeat parts (b)-(f) using an ad valorem tax of 250=3 percent on ps .

5. State True or False and then explain.
(a) For the same per unit tax, the higher the elasticity of supply the
higher would be the excess burden.
(b) If the compensated demand curve is perfectly inelastic, the excess
burden is zero.
(c) The higher the elasticity of demand, the greater will be the incidence
of a tax on consumers.
(d) The lower the elasticity of supply, the smaller will be the incidence
of a tax on consumers
(e) For the same per unit tax, the lower the elasticity of supply the higher
would be the tax revenues.
(f) The higher the tax rate (on a given commodity), the higher will be
the tax revenue.

6. Assume that in the absence of taxes, the price of x is $2. Compare an
ad valorem tax of 10 percent (on ps ), to a per unit tax of 20 cents with
respect to (i.e. specify whether it results in bigger, smaller, or equal values
of the following):
(a) the new equilibrium consumer price
(b) the new equilibrium producer price
(c) the new equilibrium value of the quantity purchased.
(d) tax revenue
(e) excess burden.

7. Assume that the inverse demand and supply curves are given by
pc
p s = 15 x = :5x Do not distinguish between ordinary and compensated demand in answering these questions.
(a) Draw these curves.
2 (b) Suppose initially pc = ps = 5. Find the consumer and the producer
surplus at this price.
(c) Suppose the government gives a subsidy of $3 per unit of output on
the consumption of x. Find x; pc , and ps . Find the consumer and
the producer surplus at this price.
(d) Find the change in the consumer and in the producer surplus in going
from (b) to (c) in the above.
(e) Find the net welfare change in going from (b) to (c). Indicate whether
this is a gain or loss.

8. The following linear functions denote the demand and supply functions
for good x.
xd = 20 xs = ps pc There is an ad-valorem tax on at the rate of on ps . Do not distinguish
between ordinary and compensated demand in answering these questions.
(a) Derive the equilibrium values of the quantity, producer price, and
consumer price as a function of .
(b) Derive the tax revenue function, R( ).
(c) Draw R( ) and determine at what tax rate, the tax revenue is maximized.
(d) Derive the marginal tax revenue function, M T R:
(e) Derive an expression for excess burden, EB, as function of the tax
rate .
(f) Derive an expression for marginal excess burden, M EB, as a function
of .
(g) At what tax rate is excess burden minimized? At what rate is it
maximized?
(h) Derive an expression for marginal excess burden per marginal tax
revenue, M EB=M T R.
(i) Show that M EB=M T R is increasing in .

9. Assume a monopoly faces a linear demand curve given by q = 45 p,
where q is quantity and p is consumer price. (This means that marginal
revenue function is M R = 45 2q). Marginal cost, M C, of producing the
output is $5. By how much does the consumer price go up if we levy a $2
tax on this good? 3