Question

Suppose the demand for good X can be represented by the following equation: QX = 50 - 1.25P. Furthermore, suppose that the demand for good Y can be represented by QY = 20 - 0.5P. a. Find the elasticity of demand for both good X and good Y when the price of X is $10 and the price of Y is $15. b.If the community’s goal is to raise tax revenue as efficiently as possible, what should be the ratio of the tax on X to the tax on Y? (Hint: You can use the regular elasticity formula to calculate the elasticity. Elasticity at a given price can also be found using the formula: elasticity = - (1/s)(P/QX), where s is the slope of the inverse demand curve, QX is the quantity demanded, and P is the price. )

Answer #1

**(a)** The elsticity of X would be as
or
or
or
or
, and for the price $10 and quantity
, we have the elasticity as
or
.

The elsticity of X would be as or or or or , and for the price $15 and quantity , we have the elasticity as or .

**(b)** The after tax demand would be
and
, and the tax revenues would be
and
. The tax revenue maximization problem would be to maximize
with respect to tx and ty.

The FOCs would be as below.

or or or .

or or or .

Solving for the FOCs, we have , which is the optimal ratio of tax on X and tax on Y that maximizes the total revnue T.

Suppose the relationship between Demand for good x (Qx) can be
described by the following linear relationship (Py: price of good
y, I = income):
Qx= 120 – 6Px + 5Py + 3 I
From the demand relationship above, you can conclude: Goods X
and Y are substitute/complementary goods
because_______________________, and a decrease in Py would cause
quantity demanded/demand of Good X to increase/decrease.
Suppose Py = $5 per unit, and I = $10, and Px = $20. At these...

Suppose the demand curve for good X is of the form:
qx=1000 + I – 50px -20py. Suppose,
px=$10, py=$10, and income (I)=$100.
1)
Cross price elasticity of demand between X and Y = -1/2, and X
and Y are complements.
2)
Cross price elasticity of demand between X and Y = 1/2, and X
and Y are complements.
3)
Cross price elasticity of demand between X and Y = -1/2, and X
and Y are substitutes.
4)
Cross price...

Suppose the demand function for ice cream (good X) is given by
Qx^d= 1200-5Px-0.08Pz+0.04M+3A where Px =$40, Px=$100, M=3000, A=
700, Z is a related good, M is income and A is the level of
advertising. •determine the own price elasticity, and whether the
demand is elastic, inelastic, or unitary elastic? What should
managers do to increase their profits? • determine the cross price
elasticity between good X and good Z and state whether they are
substitutes, or complements and...

Suppose the demand for good X has estimated to be:
lnQxd = 10 - 4lnPx –
2lnPy – 4 lnM.
a. How can you tell that demand is downward sloping?
b. What is the cross-price elasticity of demand between good X
and Y?
c. Are good X and Y substitutes or complements?
d. Is good X a normal or an inferior good?
e. If the price of good X increased by 2 percent, what would
happen to the quantity demanded...

Suppose a firm has an estimated general demand function for good
X is given by:
Q = 200,000 -500P + 1.5M – 240Pr
Where P = price of good X, M is the average income of the
consumers who buy good X, and Pr is the price of a related good.
Suppose that the values of P, M and Pr are given by $200, $80,000,
and $100 respectively.
An increase in the price of good X by 5% will
Decrease...

2. Given a demand equation for goods X:
?? = 50 − 0.4?? + 0.02? + 0.1??
a. How much is the quantity demanded if price of goods x (PX) is
RM50, income (Y) RM6000 and price of goods z (Pz) is RM60?
b. Calculate price elasticity of demand for good x when its price
is RM50. Is the demand for good x sensitive to the change in its
price?
c. Determine the cross elasticity of demand for good x...

Suppose the quantity of good X demanded by consumer 1 is given
by: Q DX1 =62 – 3P X + 0.35I + 0.3P Y And the quantity of good X
demanded by consumer 2 is given by: Q DX2 = 10 – 2.5P X + 0.2I +
0.6P Y Answer the following questions and ensure that you show ALL
calculations.
(a) What is the market demand for good X? 3 marks
(b) Using the first demand function: (Q DX1 =...

a-Define the demand function of a good and its price elasticity
of demand.
b- Suppose that the government wants to maximize tax revenue.
Explain why it may be not a good idea for the government to raise
tax rates for a good with a price elasticity of demand more than
one.

Suppose the demand function for good X is estimated to be Qdx =
1000 – 25Px + 10Py + 100M, where Qdx is quantity demanded of X, Px
is the price of good X, Py is price of some other good Y, and M is
the average income of consumers. By examining this function, we can
say good X has a downward sloping demand curve, is a substitute
with good Y, and is a normal good.

Suppose the demand function for good X is estimated to be Qdx =
1000 – 25Px + 10Py + 100M, where Qdx is quantity demanded of X, Px
is the price of good X, Py is price of some other good Y, and M is
the average income of consumers. By examining this function, we can
say good X has a downward sloping demand curve, is a substitute
with good Y, and is a normal good.

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