b) Upon leaving the shop, Kante buys orange juice and yoghurt for the family. If he earns €100 a week and the price of orange juice is €2 a carton, while yoghurt is priced at €4 a tub. What quantity will he be able to buy if he decides to all his income o
To analyze Kante's budget constraints, we will break it down into parts (b) and (c), and provide graphical representations.
### Part b: Initial Budget Constraint
Kante earns €100 a week. Let's determine how much orange juice and yoghurt he could buy if he spent all his income on each.
1. **Price of Orange Juice:** €2 per carton
2. **Price of Yoghurt:** €4 per tub
**Maximum Quantity Calculation:**
- **All income on Orange Juice:**
- Maximum cartons = Total income / Price of orange juice
- Maximum cartons = €100 / €2 = 50 cartons
- **All income on Yoghurt:**
- Maximum tubs = Total income / Price of yoghurt
- Maximum tubs = €100 / €4 = 25 tubs
**Budget Constraint Equation:**
The budget constraint can be expressed as:
\[ P_{\text{OJ}} \cdot Q_{\text{OJ}} + P_{\text{Y}} \cdot Q_{\text{Y}} = I \]
Where:
- \( P_{\text{OJ}} \) = Price of orange juice = €2
- \( P_{\text{Y}} \) = Price of yoghurt = €4
- \( Q_{\text{OJ}} \) = Quantity of orange juice
- \( Q_{\text{Y}} \) = Quantity of yoghurt
- \( I \) = Income = €100
The equation becomes:
\[ 2Q_{\text{OJ}} + 4Q_{\text{Y}} = 100 \]
**Graph: Budget Constraint**
- The x-axis represents Orange Juice (Q_OJ).
- The y-axis represents Yoghurt (Q_Y).
1. When \( Q_{\text{OJ}} = 50 \) (intercept on the x-axis, 0 tubs of yoghurt)
2. When \( Q_{\text{Y}} = 25 \) (intercept on the y-axis, 0 cartons of orange juice)
Graphically, you would draw a straight line connecting the two points, showing the trade-off between spending on orange juice and yoghurt.
### Part c: New Budget Constraint after Price and Salary Increase
In 2022, the prices of both commodities and Kante’s salary increase by 10%.
1. **New Prices:**
- Orange Juice: €2 + 10% of €2 = €2 + €0.2 = €2.20
- Yoghurt: €4 + 10% of €4 = €4 + €0.4 = €4.40
2. **New Income:**
- Kante's new salary = €100 + 10% of €100 = €100 + €10 = €110
**New Maximum Quantity Calculation:**
- **All income on Orange Juice:**
- Maximum cartons = €110 / €2.20 ≈ 50 cartons (exact amount = 50.0 cartons)
- **All income on Yoghurt:**
- Maximum tubs = €110 / €4.40 ≈ 25 tubs (exact amount = 25.0 tubs)
**New Budget Constraint Equation:**
Following the previous format,
\[ 2.20Q_{\text{OJ}} + 4.40Q_{\text{Y}} = 110 \]
**Graph of the New Budget Constraint:**
- The same axes apply here, but the intercepts have shifted:
1. When \( Q_{\text{OJ}} = 50 \) with €2.20 price (intercept on the x-axis)
2. When \( Q_{\text{Y}} = 25 \) with €4.40 price (intercept on the y-axis)
**Graphically,** this new line will shift inward or remain the same as the initial line depending on the trade-off ratios, but here they maintain the same maximum quantities, reflecting the uniform increase in both prices and income.
### Summary
In summary, after the increases in prices and salary, Kante's budget constraint remains linear, but the value of commodities relative to his budget supports different potential quantities both before and after price adjustments. This provides an illustration of how economic factors such as inflation affect purchasing power alongside income changes.