a) Given that utility is the level of satisfaction a consumer drives from consuming a commodity, and assuming that economic agents are rational and prefer more to less. Explain what might be observed about the total utility and marginal utility of Kante w

### a) Total Utility and Marginal Utility In the context of Kante visiting a coffee shop for four cups of black coffee, we can analyze the total utility and marginal utility associated with his consumption. 1. **Total Utility**: Total utility is the overall satisfaction derived from consuming a number of goods. When Kante has his first cup of black coffee, he experiences a high level of satisfaction, leading to a high total utility. As he consumes the second, third, and fourth cups, total utility continues to rise, but typically at a decreasing rate. 2. **Marginal Utility**: Marginal utility is the additional satisfaction gained from consuming one more unit of a good. With each subsequent cup of coffee, the marginal utility tends to decline; that is, the satisfaction Kante derives from the third cup is likely less than that derived from the second cup, and so on. This phenomenon is consistent with the **Law of Diminishing Marginal Utility**, which states that as a consumer consumes more units of a good, the additional satisfaction from each successive unit will eventually decrease. 3. **Pricing**: As a result of diminishing marginal utility, consumers are often unwilling to pay the same price for each successive unit. For example, Kante may be willing to pay €3 for his first cup of coffee, €2.50 for the second, and even less for the third and fourth cups, reflecting the decreasing additional satisfaction they provide. ### b) Kante’s Budget and Consumption Kante earns **€100 a week**. The price of orange juice is **€2** (per carton), and the price of yogurt is **€4** (per tub). To find out how much Kante can buy if he spends all his income on each commodity: 1. **If he buys only orange juice**: \[ \text{Number of cartons of orange juice} = \frac{€100}{€2} = 50 \text{ cartons} \] 2. **If he buys only yoghurt**: \[ \text{Number of tubs of yoghurt} = \frac{€100}{€4} = 25 \text{ tubs} \] #### Budget Constraint Graph To illustrate Kante's budget constraint, plot the axes as follows: - The **x-axis** represents the quantity of orange juice. - The **y-axis** represents the quantity of yoghurt. Kante's budget line can be represented by the equation: \[ 2Q_{oj} + 4Q_{y} = 100 \] Where \(Q_{oj}\) is the quantity of orange juice and \(Q_{y}\) is the quantity of yoghurt. The intercepts can be calculated: - At \(Q_{y} = 0\): \(2Q_{oj} = 100 \rightarrow Q_{oj} = 50\) - At \(Q_{oj} = 0\): \(4Q_{y} = 100 \rightarrow Q_{y} = 25\) The budget constraint would then be a straight line connecting (50, 0) with (0, 25). ### c) New Budget Constraint after Price Changes If all prices increase by 10%, the new prices will be: - **Orange Juice**: \(€2 \times 1.10 = €2.20\) - **Yoghurt**: \(€4 \times 1.10 = €4.40\) With Kante's salary increasing by 10%, his new income will be: - **Income**: \(€100 \times 1.10 = €110\) The new budget constraint equation is: \[ 2.20Q_{oj} + 4.40Q_{y} = 110 \] Calculating intercepts for the new budget line: - At \(Q_{y} = 0\): \[ 2.20Q_{oj} = 110 \rightarrow Q_{oj} = \frac{110}{2.20} \approx 50 \] - At \(Q_{oj} = 0\): \[ 4.40Q_{y} = 110 \rightarrow Q_{y} = \frac{110}{4.40} \approx 25 \] The new budget line will retain similar intercepts since the price increase occurred with an equal percentage change in income. ### d) Effect of Price and Income Changes The price increases and corresponding salary increase lead to a few important observations: 1. **New Budget Constraint**: The slope of the budget line (the relative prices of the goods) remains unchanged, indicating that the trade-off ratio between orange juice and yogurt remains the same. 2. **Purchasing Power**: Even though Kante's income increased commensurately with the prices, his purchasing power has effectively remained the same from the perspective of making choices between the two goods. He can still purchase the same combinations of goods as before, but the cost per unit has risen. 3. **Consumer Behavior**: Changes in relative utility or preferences may lead Kante to reassess his consumption bundle even though he has the same purchasing power. Overall, the changes do not affect Kante's overall budget constraint structure, but it could lead to changes in behavioral consumption choices depending on his utility preferences.