
(a)
Whether the assumption 'more is better' satisfied for both the goods, x and y or not.

Explanation of Solution
The consumer prefers two goods x and y.
The utility function of the consumer is given as follows-
Also,
The additional utility derived from the consumption of additional unit of good is known as marginal utility.
Since, MUx > 0 and MUy> 0. The assumption that more is better is satisfied for both the goods.
(b)
Whether the marginal utility of good x diminishes, remain constant, or increase as the consumer buys more units of good x.

Explanation of Solution
Differentiate (1) with respect to x to determine whether the marginal utility good x diminishes, remain constant, or increase as the consumer buys more units of good x.
As,
Thus, it can be concluded that marginal utility of good x diminishes as the consumer buys more units of good x.
(c)
Marginal rate of substitution of the two goods, x and y.

Explanation of Solution
The rate at which consumer is willing to sacrifice some units of good x to get an additional unit of good y is known as marginal rate of substitution (MRS).
MRSx,y, is equal to the ratio of the marginal utility of good x to the marginal utility of good y.
(d)
Whether marginal rate of substitution of the two goods, x and y diminishes, remain constant, or increase as the consumer substitutes x for y along an indifference curve.

Explanation of Solution
Differentiate (3) with respect to x to determine whethermarginal rate of substitution of the two goods, x and y diminishes, remain constant, or increase as the consumer substitutes x for y along an indifference curve.
As,
Thus, it can be concluded that marginal rate of substitution of the two goods, x and y diminishes, as the consumer substitutes x for y along an indifference curve.
(e)
A typical indifference curve of the given utility function. And whether the curve intersects X-axis or Y-axis or not.

Explanation of Solution
The figure (1) below depicts a typical indifference curve U1. The declining slope of the curve represents diminishing MRSx, y.
The indifference curve U1 does not intersect either axis.
(f)
The second indifference curve U2, with U2> U1.

Explanation of Solution
The figure (2) below represents second indifference curve U2. Here, U2 >U1.
Since U2 lies above U1,U2 represents higher level of satisfaction. Thus, U2 >U1. A consumer always prefers higher indifference curves.
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Chapter 3 Solutions
EBK MICROECONOMICS
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