C) Calculate and interpret price elasticity of demand at the equilibrium point.

Question

6. When price of tea in local café rises from Br. 10 to 15 per cup, demand for coffee rises
from 3000 cups to 5000 cups a day despite no change in coffee prices.
A) Determine cross price elasticity.
B) Based on the result, what kind of relation exists between the two goods?
7. What is the basic difference between cardinal and ordinal approaches of utility?
8. A rational consumer spends all of her income on two goods: Apple and Banana.
Suppose the last dollar spent on Apple increased her total utility from 60 utils to 68 utils
and the last dollar spent on Banana increased her total utility from 25 utils to 29 utils. If
the price of a unit of Apple is 2 Birr, what is the price of a unit of Banana at equilibrium?�

Answer 1

C) To calculate price elasticity of demand at the equilibrium point, we need the initial quantity demanded, final quantity demanded, initial price, and final price. In this case, the initial price of tea is Br. 10 per cup, and the final price is Br. 15 per cup. The initial quantity demanded is 3000 cups, and the final quantity demanded is 5000 cups.

The formula for price elasticity of demand is:

E = ((Q2 - Q1)/(Q2 + Q1))/((P2 - P1)/(P2 + P1))

Using the values given:

E = ((5000 - 3000)/(5000 + 3000))/((15 - 10)/(15 + 10))
E = (2000/8000)/(5/25)
E = (1/4)/(1/5)
E = 5/4

The price elasticity of demand at the equilibrium point is 5/4. This means that for a 1% increase in price, demand will decrease by 1.25%.

A) To determine the cross price elasticity, we need the initial quantity demanded of coffee, final quantity demanded of coffee, and the price of tea.

The initial quantity demanded of coffee is 3000 cups, and the final quantity demanded of coffee is 5000 cups. The price of tea is Br. 10 per cup.

The formula for cross price elasticity is:

Exy = ((Q2y - Q1y)/(Q2y + Q1y))/((P2x - P1x)/(P2x + P1x))

Using the values given:

Exy = ((5000 - 3000)/(5000 + 3000))/((15 - 10)/(15 + 10))
Exy = (2000/8000)/(5/25)
Exy = (1/4)/(1/5)
Exy = 5/4

The cross price elasticity is also 5/4.

B) Based on the result of the cross price elasticity, a positive cross price elasticity indicates that tea and coffee are substitutes. When the price of tea increased, the demand for coffee increased, suggesting that consumers are switching from tea to coffee.

7. The basic difference between the cardinal and ordinal approaches of utility is how they measure utility.

In the cardinal approach, utility is measured quantitatively and can be assigned numerical values, such as utils. This approach assumes that utility can be objectively measured and compared between different individuals. It is based on the assumption that individuals can rank their preferences and make precise comparisons between different levels of utility.

In contrast, the ordinal approach of utility does not assign numerical values to utility. Instead, it focuses on the ordering or ranking of preferences. It assumes that individuals can only compare and rank different options based on their preference. This approach does not make assumptions about the magnitude of the differences in utility between different options, only that individuals can identify their preferred choice.

8. To determine the price of a unit of Banana at equilibrium, we need to compare the utility per dollar spent on Apple and Banana.

The increase in utility for the last dollar spent on Apple is from 60 utils to 68 utils, which is an increase of 8 utils. The increase in utility for the last dollar spent on Banana is from 25 utils to 29 utils, which is an increase of 4 utils.

The price of a unit of Apple is 2 Birr. Since the increase in utility for the last dollar spent on Apple is 8 utils, and the price of Apple is 2 Birr, the utility per Birr spent on Apple is 8/2 = 4 utils per Birr.

To find the price of a unit of Banana at equilibrium, we compare the utility per Birr spent on Banana, which is 4 utils per Birr. Therefore, the price of a unit of Banana at equilibrium should also be 2 Birr.