Question

Qdx = 2500 - 0.5 Px + 0.75 Py + 2.0 I, given that Px = $ 400, Py = $ 200 and I = $ 1500

Question:
a.Calculate the price elasticity for good X and what is the economic meaning of the number, explain!
b. Calculate the cross elasticity between goods X and Y and the income elasticity of good X and what is the economic meaning of the number, just put!
c. If the price of goods X increases by 10% ceteris paribus then recalculate questions a and b above, explain!
d. And what are the consequences of the increase in price, question c, on consumer expenditures for goods X, explain as necessary! According to you, is the relationship between goods X and Y substitution or complementary and according to you, item X is. Inferior (KW) or Ori, explain !?
e. If you know Px = $ 5000, ceteris paribus then calculate how much consumer surplus at that time, explain! And how much will the consumer surplus be if Px goes up to $ 6,000 ceteris paribus? What conclusion did you reach by comparing the two numbers!
f.Describe the above problem into the graph!

Answer 1

We have the following information

Q = 2500 – 0.5Px + 0.75Py + 2.0I

Q = Quantity

Px = Price of X = $400

Py = Price of Y = $200

I = Income = $1500

1) Price elasticity of X = (ΔQ/ΔPx) × (Px/Q)

ΔQ/ΔPx = – 0.5

Px = $400

Q = 2500 – (0.5 × 400) + (0.75 × 200) + (2.0 × 1500)

Q = 2500 – 200 + 150 + 3000

Q = 5650 – 200

Q = 5450

Price elasticity of X = (– 0.5) × (400/5450)

Price elasticity of X = – 0.037

Since, the price elasticity is less than one so we can say that the demand for Good X is inelastic. The negative sign indicates that as the price increases the demand for good X declines and vice-a-versa.

2) The cross-elasticity of demand is defined as the proportionate change in the quantity demanded of a good 1 due to a proportionate change in the price of another good 2.

Cross price elasticity = (ΔQ/ΔPy) × (Py/Q)

ΔQ/ΔPy = 0.75

Py = 200

Q = 5450

Cross price elasticity = (0.75) × (200/5450)

Cross price elasticity = + 0.028

The positive sign indicates that as the price of good Y increases the demand for good X increases and when the price of good Y decreases the demand for good X decreases.

Income elasticity = (ΔQ/ΔI) × (I/Q)

ΔQ/ΔI = 2.0

I = 1500

Q = 5450

Income elasticity = (2) × (1500/5450)

Income elasticity = + 0.550

The positive sign indicates that as the income increases the demand for good X increases and when income decreases the demand for good X declines.

3) It is given that the price of Good X has increased by 10%

New Px = Old Px(1 + 0.1)

New Px = 400(1 + 0.1)

New Px = 440

Price elasticity of X = (– 0.5) × (440/5450)

Price elasticity of X = – 0.040

The cross price elasticity and income elasticity will remain the same.

4) Since, the price elasticity of good X is negative so the consumer expenditure on good X will decline in response to the increase in the of good X by 10%.

Since, the cross price elasticity is positive so we can say that the relationship between good X and good Y is that of substitution. As the price of good Y increases the consumer shifts to good X because of which its demand increases.

Since, the price elasticity of demand for good X is negative and income elasticity of demand for good X is positive so we can say that good X is normal good.