Question

In: Economics

For Questions 1 and 2, the demand function for apples is given by Q = 10000...

For Questions 1 and 2, the demand function for apples is given by Q = 10000 – 1000p + 0.5M + 500po – 100pk, where Q = quantity of apples p = price of apples M = average income of consumers po = price of oranges pk = price of caramel

According to this demand function, apples are

Select one:

a. a inferior good.

b. a Giffen good.

c. a luxury.

d. a necessity.

e. a Cobb-Douglas good.

According to this demand function, apples and oranges are ___, and apples and caramel are ____.

Select one:

a. substitutes; substitutes

b. substitutes; complements

c. substitutes; neither substitutes nor complements

d. complements; substitutes

e. complements; complements

f. complements; neither substitutes nor complements

g. neither substitutes nor complements; substitutes

h. neither substitutes nor complements; complements

i. neither substitutes nor complements; neither substitutes nor complements

Solutions

Expert Solution

Demand function: Q = 10000 - 1000p + 0.5M + 500po - 100pk

Income elasticity of demand is the responsiveness of change in quantity demanded due to a change in the income of the consumers. It is given by the following formula:

Income elasticity of demand = % change in quantity demanded/ % change in income of the consumer.

OR

Income elasticity of demand = * (M/Q)

where is the partial differentiation of demand function with respect to the average income of the consumer, Q is the number of apples and M is the average income of the consumer

Income elasticity of demand = 0.5 *(M/Q)

Since the value is positive, the good is a normal good. And since the value is less than 1, this good is a necessity.

Inferior goods are the ones that have an indirect relationship with the income of the consumers. Suppose an employee who takes a bus to go to work gets a promotion and then he switches from bus to cab. The bus here will be considered as the inferior good since its demand decreased with the increase in income of the consumer.

Normal goods are the ones that have a direct relationship with the income of the consumers. Goods like food items, furniture, clothes, etc. The demand for these goods increases as the income of the consumers' increases. Normal goods are of two types, necessity, and luxury goods.

Income elasticity of necessity goods is less than 1 (it is less than 1 because the demand for these goods is not much affected by the income of the consumer). Even if the income decreases a bit, consumers will consume the necessary goods like bread, eggs, etc.

Income elasticity of luxury goods is more than 1 (this is because the change in income largely affects the purchase of luxury goods).

Cross price elasticity of demand is the responsiveness of change in quantity demanded of one good by the change in the price of another good. It is given by the following formula:

Cross price elasticity of demand for good A = % change in quantity demanded of good A/ % change in the price of good B

OR

Cross price elasticity of demand = * (Py/Q)

where is the partial differentiation of demand function with respect to the price of another good, Q is the quantity demanded of a good and Py is the price of another good.

If the value of the cross-price elasticity of demand is positive then the goods will be substitutes. Substitutes are the goods that are used in place of one another like tea and coffee.

If the price elasticity of demand is negative then the goods are complements. Complement goods are the ones that are bought together like cars and petrol, refill and pen, etc.

Cross price elasticity of apples with respect to prices of orange is: *(Po/Q)

where Po is the price of oranges and Q is the quantity demanded of apples.

Cross price elasticity of apples with respect to oranges = 500* (Po/Q)

Since the value of positive, we can say that apples and oranges are substitutes.

Cross price elasticity of apples with respect to caramel is: * (Pk/Q)

where Pk is the price of caramel.

Cross price elasticity of apples with respect to caramel = -100 * (Pk/Q)

Since the value is negative, apples and caramel are complementary goods.


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