Utility：练习题

In marginal utility theory, the individual demand curve is derived from the marginal utility curve. If a consumer experiences a decrease in the price of a good, which of the following best describes the process of reaching a new equilibrium position, assuming the marginal utility of money is constant?

Which of the following statements correctly identifies the mathematical relationship between Total Utility (TU) and Marginal Utility (MU)?

A consumer's total utility (TU) for Good X is represented by the function \( TU = 120X - 10X^2 \). If the market price of Good X is \( \$40 \) and the marginal utility of money is constant at \( 1 \), what is the consumer's optimal consumption level of X?

A consumer derives satisfaction from consuming units of a good. The table shows the total utility (\(TU\)) gained at different levels of consumption.

\(\begin{array}{|c|c|}\hline \textbf{Quantity consumed (units)} & \textbf{Total utility (units)} \\ \hline 1 & 14 \\ 2 & 26 \\ 3 & 36 \\ 4 & 44 \\ 5 & 50 \\ \hline \end{array}\)

What is the marginal utility of consuming the \(4\text{th}\) unit of the good?

According to the law of diminishing marginal utility, what occurs as a consumer increases the consumption of a good, ceteris paribus?

Define the law of diminishing marginal utility and explain its effect on a consumer's total utility as consumption of a good increases sequentially.

Analyze the relationship between the equi-marginal principle and the derivation of an individual's demand curve when the price of one good falls, assuming the Marginal Utility of money remains constant.

Using the equi-marginal principle, identify the mathematical condition required for a consumer to maximize their total utility when choosing between Good A and Good B with prices \( P_A \) and \( P_B \).

(a) Define the terms Total Utility and Marginal Utility, and explain the relationship between them.

(b) A consumer derives utility from consuming bars of chocolate. The total utility (\(TU\)) for the first four bars is given as follows: 20, 35, 45, and 50 units respectively. Calculate the marginal utility (\(MU\)) for each additional bar and explain whether this data supports the Law of Diminishing Marginal Utility.