Question

Using the utility-maximization rule as your point of reference, explain the income and substitution effects of an increase in the price of product \(\mathrm{B}\), with no change in the price of product A.

Short answer

An increase in the price of product B leads to substituting product A due to the substitution effect, and altered purchasing power due to the income effect.

Step-by-step solution

Understanding the Utility-Maximization Rule

The utility-maximization rule states that consumers aim to allocate their income in ways that maximize their overall utility or satisfaction. This happens when the consumer has allocated their income such that the last unit of currency spent on each product provides the same level of additional utility, expressed as \( \frac{MU_A}{P_A} = \frac{MU_B}{P_B} \), where \( MU \) stands for marginal utility and \( P \) is the price of the product.

Effect of Price Increase on Product B

When the price of product \( B \) increases, the equation \( \frac{MU_B}{P_B} \) decreases, disrupting the balance required by the utility-maximization rule. The consumer now receives less utility for the same expenditure on product \( B \), and this prompts a reallocation of their spending.

Substitution Effect

The substitution effect occurs when the consumer reacts to the relative change in prices by purchasing more of the relatively cheaper product. Since the price of product \( B \) has increased while the price of product \( A \) has not changed, the consumer substitutes product \( B \) with product \( A \), increasing the quantity of \( A \) purchased.

Income Effect Explanation

The income effect reflects how the change in real income, caused by the price increase, impacts the consumer's purchasing power. The rise in the price of product \( B \) reduces the consumer's real income as they can now afford less than before, potentially leading them to buy less of both products \( A \) and \( B \), depending on whether these products are viewed as normal or inferior goods by the consumer.

Overall Impact Interpretation

The overall impact of a price increase in product \( B \) on a consumer's purchase decisions is a combination of the substitution and income effects. If product \( A \) is a close substitute and the substitution effect is strong, you may see a significant increase in \( A \'s \) consumption. Conversely, if the income effect is strong and \( B \) is a normal good, there might be an overall reduction in the consumption of both products.

Key concepts

Income Effect

Whenever a price of a product like product B rises, the income effect kicks in to show how the price change alters the consumer's real income or purchasing power. Imagine you have a set budget for shopping for the month. If prices suddenly increase, your monthly budget seemingly buys less than before, reducing your purchasing power. This is because the increase in the price of product B doesn't mean you have more money; it just eats into how much you can buy with the money you have. This reduced purchasing power may lead consumers to buy less of both products A and B if both are seen as crucial to their needs.

• If both products A and B are normal goods (ones we buy more of when our income is high), the consumer might cut back on purchasing them because they feel poorer after the price increase.
• If one or both are inferior goods (ones we buy less of as our incomes rise), they might buy more of the cheaper product.

The income effect focuses on this shift in real income and its impact on buying behavior.

Substitution Effect

The substitution effect helps explain how consumers adjust their spending in response to changes in relative prices. With the price of product B increasing, it becomes more expensive compared to product A. Consequently, consumers might decide to purchase more of product A because it gives them more "bang for their buck," or utility per dollar spent. Even if the consumer didn’t initially prefer product A as much, they might still buy more of it simply because it is relatively cheaper.

• The substitution effect highlights our natural tendency to choose cheaper alternatives when prices change.
• This is especially true if products A and B are easily swappable for each other or if the consumer doesn't have a strong preference for one over the other.

The central idea is that consumers pivot towards a relatively affordable product, reinforcing the balance sought by the utility-maximization rule.

Marginal Utility

Marginal utility is a cornerstone concept that underpins how we make decisions based on our satisfaction levels from each additional unit of a product we consume. When utilizing the utility-maximization rule, we aim for each dollar spent to provide the highest possible marginal utility. An increase in the price of product B leads to a drop in its marginal utility per dollar spent \( \frac{MU_B}{P_B} \), prompting consumers to rethink their spending habits.

• To maximize utility, consumers will assess whether they get equivalent satisfaction for the money spent on both products A and B.
• If product B fails to provide as much utility due to its higher price, consumers may allocate their spending to other products offering better value, like product A in this scenario.

Understanding marginal utility allows us to comprehend how and why consumers reposition their purchases for maximum satisfaction amid changing prices.