Question

Maya spends her \(\$ 50\) budget on two goods, cans of tuna and bottles of ginger ale. Initially, the marginal utility per dollar she spends on tuna is equal to the marginal utility per dollar she spends on ginger ale. Then the price of ginger ale decreases, while her income and the price of tuna do not change. Determine whether each of the following statements about what happens as a result of the decrease in the price of ginger ale is true or false and briefly explain why. a. Her marginal utility from consuming ginger ale increases. b. The marginal utility per dollar she spends on ginger ale increases. c. Because of the substitution effect, Maya will buy more ginger ale. Therefore, we can conclude that ginger ale is a normal good. d. As Maya adjusts to the change in the price of ginger ale, her marginal utility per dollar spent on tuna will increase.

Short answer

a. False - Marginal utility doesn't increase with a decrease in price. B. True - Marginal utility per dollar increases when price decreases. C. True - The substitution effect means Maya will buy more ginger ale, and so ginger ale is a normal good. D. False - The marginal utility per dollar spent on tuna doesn't change as the price of ginger ale changes.

Step-by-step solution

Analyzing Statement a

The statement implies that Maya's marginal utility from consuming ginger ale increases. This is false because the marginal utility from an extra unit of a good typically decreases as more of the good is consumed (a concept known as diminishing marginal utility). The decrease in price does not directly increase the satisfaction (utility) Maya gets from an additional unit of ginger ale, so this is not automatically true.

Analyzing Statement b

The statement posits that the marginal utility per dollar she spends on ginger ale increases. This is true because when the price of a good decreases, the marginal utility per dollar spent on that good increases. This is because the same satisfaction is now achievable with less money, so the satisfaction per dollar is higher.

Analyzing Statement c

This statement suggests that because of the substitution effect, Maya will buy more ginger ale and hence, ginger ale can be concluded as a normal good. This is true. The substitution effect states that as the price of a good falls, consumers will tend to buy more of it because it's relatively cheaper compared to other goods. And since Maya buys more ginger ale when it becomes cheaper, ginger ale behaves as a normal good for her (the demand for normal goods increases with decrease in price).

Analyzing Statement d

The statement suggests that as Maya adjusts to the change in the price of ginger ale, her marginal utility per dollar spent on tuna will increase. This is false. The change in price of ginger ale does not affect the marginal utility from tuna or the price of tuna. Thus, the marginal utility per dollar spent on that tuna stays the same. Given that she is holding her consumption of tuna constant, the marginal utility per dollar spent on tuna shouldn't increase.

Key concepts

Diminishing Marginal Utility

In economics, the principle of diminishing marginal utility states that as a person consumes more units of a good or service, the satisfaction gained from consuming an additional unit, known as marginal utility, decreases. The first slice of pizza may bring a great deal of pleasure, but as you eat more slices, the pleasure derived from each new slice is less than the pleasure from the previous one.

This concept is crucial to understanding consumer choice and demand. As the marginal utility of a good decreases, consumers are less willing to pay the same price for additional units, which in turn affects their purchasing decisions and the allocation of their limited budget.

Substitution Effect

The substitution effect is an economic term that describes how consumers replace more expensive items with less expensive alternatives when prices change while their income remains constant. This behavior is driven by the desire to maintain an optimal level of satisfaction or utility within the constraints of their budget.

For instance, if the price of coffee increases, a consumer may begin purchasing more tea, assuming tea remains relatively cheaper. The substitution effect is part of the larger price effect, which combines with the income effect to explain changes in consumer behavior due to price changes. In the exercise with Maya, when the price of ginger ale decreases, there is a substitution effect: she buys more ginger ale because it has become relatively cheaper compared to tuna, signifying a shift in her consumption pattern.

Marginal Utility per Dollar

Marginal utility per dollar is a way to measure how much satisfaction or utility a consumer gets for every dollar spent on a good or service. It helps in comparing the utility derived from different goods and making decisions on how to distribute spending to maximize overall utility. The calculation involves dividing the marginal utility by the price of the good.

As prices change or as consumers acquire more of a good, the marginal utility per dollar spent can also change. If a good becomes less expensive without a change in the inherent satisfaction it provides, the marginal utility per dollar spent will increase, as explained in the exercise where Maya experiences an increase in the marginal utility per dollar for ginger ale after its price decreases.

Normal Good

A normal good is a type of good for which demand increases as the income of the consumer increases, all other factors being constant. Even without an income change, normal goods also see an increase in demand when their prices decrease due to the income effect and substitution effect.

Going back to our exercise, Maya shows that ginger ale is a normal good for her, as she buys more of it when the price falls. Typically, normal goods have positive income elasticity of demand, meaning people buy more of them as they become richer, but even in situations where income is constant, a price drop can lead to increased consumption, as seen with Maya's choice.