Concept explainers
(A)
To explain:
The given assumption of more is better is sufficient for both goods.
Answer to Problem 3.21P
The given assumption more is better is not sufficient for both goods.
Explanation of Solution
Given that −
And,
In the above equation both MUx and MUy are greater than zero. Therefore, the given assumption more is better is not sufficient for both goods.
Introduction:
(B)
To explain:
Whether the marginal utility of x decrease, or remain constant or increase with the consumer buying more of x, if the preferences of consumer are represented by the utility function of Cobb Douglas,
Answer to Problem 3.21P
The marginal utility of x will diminish will not diminish but increases with an increase in the consumption of x by the individual.
Explanation of Solution
The given marginal utility function of x will not diminish but increases, as the individual consumes more of good x.
Introduction:
Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.
(C)
Tofind:
The MRSxy.
Answer to Problem 3.21P
After necessary derivations, the MRSxy is given by
Explanation of Solution
Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.
Through dividing the marginal utility of x with the marginal utility of y, the marginal rate of substitution can be arrived at.
Implies,
Thus, the MRS of x for y will be
Now, it can be concluded that the MRSxy will decrease when x increases, and MRSxy also will decrease when y decreases. Since, in both these cases MRSxy decreases, it stays decreasing.
(D)
To evaluate:
Whether the MRSxy will decrease or increase or remain constant, if the individual decides to substitute x for y along an indifference curve.
Answer to Problem 3.21P
After necessary observations, it can be said that the MRSxy will be diminishing.
Explanation of Solution
Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.
MRSxy, denoting the marginal rate of substitution of x for y, equaling to
(E)
To plot:
A graph with x denoted by horizontal axis and y denoted by vertical axis, an indifference curve, and to label the curve U1.
Answer to Problem 3.21P
As can be seen in the graph plotted in the next section, the indifference curve is bowed towards the origin, owing to the diminishing MRS.
Explanation of Solution
Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.
In the graph above, as explained in the requirements, it can be seen that with the diminishing MRS, the indifference curve is bowed towards the origin.
(F)
Toplot:
On the same graph, with x denoted by horizontal axis and y denoted by vertical axis, another indifference curve, U2, as U2> U1.
Answer to Problem 3.21P
As can be seen in the graph plotted in the next section, the indifference curves, U1 and U2, as U2> U1.
Explanation of Solution
Marginal utility shows the additional utility that the consumer is deriving from consuming additional units of that product or service.
In the graph above, as explained in the requirements, it can be seen that with the diminishing MRS, the indifference curves are bowed towards the origin, satisfying the rule that U2> U1.
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