C) Calculate and interpret price elasticity of demand at the equilibrium point.
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?�
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.
6. To calculate the price elasticity of demand at the equilibrium point, we use the formula:
Price Elasticity of Demand = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)
First, let's calculate the percentage change in quantity demanded:
Change in Quantity Demanded = 5000 cups - 3000 cups = 2000 cups
Percentage Change in Quantity Demanded = (Change in Quantity Demanded / Initial Quantity Demanded) × 100
= (2000 cups / 3000 cups) × 100
≈ 66.67%
Next, let's calculate the percentage change in price:
Change in Price = 15 Birr - 10 Birr = 5 Birr
Percentage Change in Price = (Change in Price / Initial Price) × 100
= (5 Birr / 10 Birr) × 100
= 50%
Now, we can calculate the price elasticity of demand:
Price Elasticity of Demand = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)
= 66.67% / 50%
= 1.33
Interpretation: The price elasticity of demand at the equilibrium point is 1.33. This means that for every 1% increase in price, the quantity demanded will decrease by 1.33%. The demand for coffee in the café is moderately elastic.
A) To determine the cross price elasticity, we use the formula:
Cross Price Elasticity = (Percentage Change in Quantity Demanded of Coffee) / (Percentage Change in Price of Tea)
The change in price of tea is from Br. 10 to 15, which is a 50% increase.
The change in quantity demanded of coffee is from 3000 cups to 5000 cups, which is a 66.67% increase.
Cross Price Elasticity = (66.67%) / (50%)
= 1.33
B) Based on the result, a cross price elasticity of 1.33 indicates that coffee and tea are substitute goods. This means that when the price of tea increases, consumers will switch to consuming more coffee.
7. The basic difference between the cardinal and ordinal approaches to utility is the way they measure and rank the satisfaction or preferences of consumers.
- Cardinal Approach: This approach assigns numerical values to utility, which means that utility is measured in specific units or quantities. It aims to measure and compare the intensity of satisfaction derived from consuming different goods or services. For example, it assigns a specific numerical value to a cup of coffee or a piece of cake.
- Ordinal Approach: This approach does not assign numerical values to utility. Instead, it focuses on ranking preferences or satisfaction. It only determines whether one good or service is preferred over another, without quantifying the degree of preference or satisfaction. For example, it determines that a consumer prefers coffee over tea, but it does not determine by how much.
8. To find the price of a unit of Banana at equilibrium, we need to calculate the Marginal Utility per Dollar for both Apple and Banana, and then compare them.
Marginal Utility per Dollar = (Change in Total Utility) / (Change in Money Spent)
For Apple:
Change in Total Utility = 68 utils - 60 utils = 8 utils
Change in Money Spent = $2
Marginal Utility per Dollar for Apple = 8 utils / $2 = 4 utils
For Banana:
Change in Total Utility = 29 utils - 25 utils = 4 utils
Change in Money Spent = ?
Marginal Utility per Dollar for Banana = 4 utils / (Change in Money Spent)
Since we don't have the specific change in money spent for Banana, we cannot calculate the Marginal Utility per Dollar for Banana. Therefore, we cannot determine the price of a unit of Banana at equilibrium.