Explain the relationship between product X, product Y and product Z or the properties of each according to the following statements

a. Cross price elasticity between X and Y is -4
b. Cross price elasticity between X and Y is 12
c. Cross price elasticity between Y and Z is 0
d. Cross price elasticity between X and Z is 0.6
e. The demand price elasticity for product X is -4
f. The demand price elasticity for product y is - 0.4
g. The Income elasticity for product X is -4
h. The Income elasticity for product Y is 0.4
i. The Income elasticity for product Z is 4

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suppose the demand for product X is estimated as:


Qdx = 7,000 – 30Px + 20Py – 18Pz – 0.5M

Where,
Px = Price of product X
Py = Price of product y
Pz = Price of Product Z
M = Income.

Assume Px = 16, Py = 10, Pz = 8 and M = RM2000

a)How many units of Product X will be purchased?
b)Derive the demand function for Product X.
c)Explain the relationship between Product X and Y.
d)Explain the relationship between Product X and Z.
Is Product X a normal or inferior good? Why?

To understand the relationships between product X, product Y, and product Z, we need to analyze the statements for their respective cross price elasticity, demand price elasticity, and income elasticity.

a. Cross price elasticity between X and Y is -4:
Cross price elasticity measures the responsiveness of the quantity demanded of one good to a change in the price of another good. In this case, a cross price elasticity of -4 suggests that a 1% increase in the price of product Y would result in a 4% decrease in the quantity demanded of product X. Therefore, product X and product Y are considered substitutes, as an increase in the price of one leads to a significant decrease in the demand for the other.

b. Cross price elasticity between X and Y is 12:
With a cross price elasticity of 12, a 1% increase in the price of product Y would cause a 12% decrease in the quantity demanded of product X. Similar to the previous statement, this indicates that product X and product Y are substitutes, as the change in price has a substantial impact on the demand for each other.

c. Cross price elasticity between Y and Z is 0:
A cross price elasticity of 0 suggests that there is no significant relationship between the price of product Y and the quantity demanded of product Z. This means that product Y and product Z are considered independent goods, where a change in the price of one has no noticeable effect on the demand for the other.

d. Cross price elasticity between X and Z is 0.6:
With a cross price elasticity of 0.6, a 1% increase in the price of product Z would lead to a 0.6% decrease in the quantity demanded of product X. This indicates a weak positive relationship between the two products, where an increase in the price of one product affects the demand for the other product to a lesser degree.

e. The demand price elasticity for product X is -4:
Demand price elasticity measures the responsiveness of the quantity demanded of a product to a change in its price. A demand price elasticity of -4 suggests that a 1% increase in the price of product X would lead to a 4% decrease in the quantity demanded of product X. This indicates that product X is price elastic, meaning that changes in price have a significant impact on the demand for the product.

f. The demand price elasticity for product Y is -0.4:
With a demand price elasticity of -0.4, a 1% increase in the price of product Y would result in a 0.4% decrease in the quantity demanded of product Y. This indicates that product Y is price inelastic, implying that changes in price have a relatively small impact on the demand for the product.

g. The Income elasticity for product X is -4:
Income elasticity measures the responsiveness of the quantity demanded of a product to a change in consumer income. An income elasticity of -4 suggests that a 1% increase in consumer income would lead to a 4% decrease in the quantity demanded of product X. Therefore, product X is considered an inferior good, as an increase in income leads to a decrease in the demand for the product.

h. The Income elasticity for product Y is 0.4:
With an income elasticity of 0.4, a 1% increase in consumer income would result in a 0.4% increase in the quantity demanded of product Y. This indicates that product Y is a normal good, as an increase in income leads to an increase in the demand for the product.

i. The Income elasticity for product Z is 4:
An income elasticity of 4 indicates that a 1% increase in consumer income would lead to a 4% increase in the quantity demanded of product Z. This suggests that product Z is a luxury good, as it experiences a substantial increase in demand as consumer income rises.

In summary, based on the given statements:
- Product X and product Y are substitutes.
- There is no significant relationship between product Y and product Z.
- There is a weak positive relationship between product X and product Z.
- Product X is price elastic, while product Y is price inelastic.
- Product X is an inferior good, while product Y is a normal good, and product Z is a luxury good.