EBK MICROECONOMICS
EBK MICROECONOMICS
5th Edition
ISBN: 9781118883228
Author: David
Publisher: YUZU
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Chapter 3, Problem 3.18P
To determine

(a)

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

Expert Solution
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Explanation of Solution

The consumer prefers two goods x and y.

The utility function of the consumer is given as follows-

  U(x,y)x0.4y0.6

Also, marginal utility of the two goods is given as follows-

   MUx0.4( x -0.6 y 0.6 )(1) MUy0.6( x 0.4 y -0.4 )(2)

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.

To determine

(b)

Whether the marginal utility of good x diminishes, remain constant, or increase as the consumer buys more units of good x.

Expert Solution
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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.

   MU x x =( 0.4 )( -0.6 ) x -0.6-1 y 0.6 =-( 0.24 ) x -1.6 y 0.6

As, MUxx<0.

Thus, it can be concluded that marginal utility of good x diminishes as the consumer buys more units of good x.

To determine

(c)

Marginal rate of substitution of the two goods, x and y.

Expert Solution
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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.

  MRSx,y= MUx MUy=0.4( x -0.6 y 0.6 )0.6( x 0.4 y -0.4 )=0.667(yx)(3)

To determine

(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.

Expert Solution
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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.

   MRS x=0.667( y x 2 )

As, MRSx<0.

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.

To determine

(e)

A typical indifference curve of the given utility function. And whether the curve intersects X-axis or Y-axis or not.

Expert Solution
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Explanation of Solution

The figure (1) below depicts a typical indifference curve U1. The declining slope of the curve represents diminishing MRSx, y.

  EBK MICROECONOMICS, Chapter 3, Problem 3.18P , additional homework tip  1

The indifference curve U1 does not intersect either axis.

To determine

(f)

The second indifference curve U2, with U2> U1.

Expert Solution
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Explanation of Solution

The figure (2) below represents second indifference curve U2. Here, U2 >U1.

  EBK MICROECONOMICS, Chapter 3, Problem 3.18P , additional homework tip  2

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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