Question

A tax is not distortionary if it has no substitution effect on consumers’ behavior. Consider a tax imposed on a product with a vertical market demand. Is this tax distortionary or not? In a diagram, illustrate the pre-tax and post-tax optimal bundles of a consumer whose purchases are not affected by a tax-induced increase in the price of good X. Use this diagram to analyze whether the tax has a substitution effect on the consumer’s purchases of X or not. Discuss.

Answer #1

A taxis considered to be distortionary (for the consumer) when a levy of tax leads to a fall in the optimal quantity of the commodity.

Considering a commodity for which the demand curve is vertical (elasticity of demand is infinite in this case) and the supply curve is upward sloping. In this case, the introduction of a tax on the product will be borne entirely by the producer. The supply curve would shift leftwards by the amount of the tax, equilibrium price would increase but the equilibrium quantity remains the same.

Thus, the tax had no effect on the consumer's purchase of X.

Diagrammatically,

E is the initial equilibrium, with corresponding quantity Q and price P. After tax, the supply curve shifts to S', equilibrium shifts to E' and the price increases to P'.

The substitution effect of a price increase:
A.
causes the consumer to purchase more of the good whose price has
risen.
B.
has no effect on the amount purchased of either good.
C.
can cause the consumer to purchase either more or less of the
good.
D.
causes the consumer to purchase less of the good that is now
relatively more expensive.
There are only three consumers in the market, and their demand
equations are as follows: (1) Q =...

3. Make a diagram illustrating the effect of a change in price
on a consumer’s optimal choice of goods x and y. Assume each
consumer has well behaved preferences, that no consumer has kinky
preferences, and that the optimal consumer choice will always be an
interior solution
a. The price of good one decreases. Assume both x and y are
normal.
b. The price of good one decreases. Assume good x is inferior
and nongiffen.

4. Suppose a consumer has perfect substitutes preference such
that good x1 is twice as valuable as to the consumer as good
x2.
(a) Find a utility function that represents this consumer’s
preference.
(b) Does this consumer’s preference satisfy the convexity and
the strong convex- ity?
(c) The initial prices of x1 and x2 are given as (p1, p2) = (1,
1), and the consumer’s income is m > 0. The prices are changed,
and the new prices are (p1,p2)...

Problem 1 [32 marks] A consumer has a demand function
for good 2, ?2, that depends on the price of good 1, ?1, the price
of good 2, ?2, and income, ?, given by ?2 = 2 + 240 ??2 + 2?1.
Initially, assume ? = 40, ?2 = 1, and ?1 = 2. Then the price of
good 2 increases to ?2 ′ = 3.
a) What is the total change in demand for good 2? [2 marks]
b)...

Suppose that a consumer has preferences over bundles of
non-negative amounts of each two goods, x1 and x2, that can be
represented by a quasi-linear utility
function of the form
U(x1,x2)=x1 +√x2.
The consumer is a price taker who faces a price per unit of good
one that is equal to $p1 and a price per unit of good two that is
equal to $p2. An- swer each of the following questions. To keep
things relatively simple, focus only on...

A consumer has a demand function for good 2, ?2, that depends on
the price of good 1, ?1, the price of good 2, ?2, and income, ?,
given by ?2 = 2 + 240/(??2) + 2?1. Initially, assume ? =40, ?2 = 1,
and ?1 = 2. Then the price of good 2 increases to ?2′ = 3.
a) What is the total change in demand for good 2?
b) Calculate the amount of good 1 consumed at the...

A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that
MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2)
a. What is the marginal rate of substitution?
b. Suppose that the price of good x is 2, and the price of good
y is 1. The consumer’s income is 20. What is the optimal quantity
of x and y the consumer will choose?
c. Suppose the price of good x decreases to 1. The price of good
y and...

A consumer has utility for protein bars and vitamin water
summarized by the Cobb-Douglas utility function U(qB,qW) =
qBqW.
a. Show that the consumer’s MRS at a generic bundle (qB,qW) is
MRS = - MUB/MUW = - qW/qB.
b. Show that the consumer’s MRS would equally be - qW/qB. if the
consumer’s utility function was V(qB,qW) = qB0.5qW0.5.
c. Find the consumer’s Marshallian demand for protein bars when
M = 100 and Pw = 1.
d. Is the demand function...

Rick purchases two goods, food and clothing. He has a
diminishing marginal rate of substitution of food for clothing. Let
x denote the amount of food consumed and y the amount of clothing.
Suppose the price of food increases from Px1 to Px2. For which of
the following cases the price effect equals the substitution
effect?
A.Food is a normal good.
B.Food is neither a normal good nor an inferior good.
C.The income elasticity of demand for food is zero....

3. Suppose that a consumer has a utility function given by
U(X,Y) = X^.5Y^.5 . Consider the following bundles of goods: A =
(9, 4), B = (16, 16), C = (1, 36).
a. Calculate the consumer’s utility level for each bundle of
goods.
b. Specify the preference ordering for the bundles using the
“strictly preferred to” symbol and the “indifferent to” symbol.
c. Now, take the natural log of the utility function. Calculate
the new utility level provided by...

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