Question

Suppose, alternatively, that leisure and consumption goods are perfect substitutes. In this case, an indiference curve is described by the equation i = al + bC, where a and b are positive constants, and u is the level of utility. That is, a given indiference curve has a particular value for u, with higher indiference curves having higher values for u. (a) Show what the consumer’s indiference curves look like when consumption and leisure are perfect substitutes, and determine graphically and algebraically what consumption bundle the consumer chooses. Show that the consumption bundle the consumer chooses depends on the relationship between a/b and w, and explain why. (b) Do you think it likely that any consumer would treat consumption goods and leisure as perfect substitutes?

Answer #1

(a) In case of perfecf substitute goods the Indifference curve will be at a constant slope. The marginal rate of substitution will be stable or constant. The consumer will be struck between the two goods at a fixed ratio. Because he/she will have the willingness for both the good at fixed rate.

The MRS will either be zero or infinite.

(b) It would have least changes because the consumer's first priority would be consumption goods. It may rare chance of being a perfect substitute because they both gove different level of satisfaction depending on the income of the consumer.

In the labor-leisure model, the representative consumer receives
satisfaction from consumption of goods (C) and from the consumption
of Leisure (L). Let C be the composite good with price $1 and L
determines the number of hours of leisure this person consumes.
Therefore U = f(C,L) for this consumer. This consumer’s consumption
is constrained by time and income. Let her non-labor income, V, be
$1200 per week, let the hourly wage rate be $8 and h be the number
of...

4. Suppose a consumer has perfect substitutes preference such
that good x1 is twice as valuable as to the consumer as good
x2.
(a) Find a utility function that represents this consumer’s
preference.
(b) Does this consumer’s preference satisfy the convexity and
the strong convex- ity?
(c) The initial prices of x1 and x2 are given as (p1, p2) = (1,
1), and the consumer’s income is m > 0. The prices are changed,
and the new prices are (p1,p2)...

1. A consumer has the utility function U = min(2X, 5Y ). The
budget constraint isPXX+PYY =I.
(a) Given the consumer’s utility function, how does the consumer
view these two goods? In other words, are they perfect substitutes,
perfect complements, or are somewhat substitutable? (2 points)
(b) Solve for the consumer’s demand functions, X∗ and Y ∗. (5
points)
(c) Assume PX = 3, PY = 2, and I = 200. What is the consumer’s
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(2 points)
2....

Suppose a consumer views two goods, X and Y, as perfect
complements. Her utility function is given by U = MIN [2X, Y].
Sketch the graph of the consumers indifference curve that goes
through the bundle X = 5 and Y = 6. Put the amount of Y on the
vertical axis, and the amount of X on the horizontal axis. Which of
the three assumptions that we made about consumer preferences is
violated in this case?

Suppose a consumer views two goods, X and Y, as perfect
complements. Her utility function is given by U = MIN [2X, Y].
Sketch the graph of the consumers indifference curve that goes
through the bundle X = 5 and Y = 4. Put the amount of Y on the
vertical axis, and the amount of X on the horizontal axis. Which of
the three assumptions that we made about consumer preferences is
violated in this case?

There are two goods, Good 1 and Good 2, with positive prices
p1 and p2. A consumer has the utility
function U(x1, x2) = min{2x1,
5x2}, where “min” is the minimum function, and
x1 and x2 are the amounts she consumes of
Good 1 and Good 2. Her income is M > 0.
(a) What condition must be true of x1 and
x2, in any utility-maximising bundle the consumer
chooses? Your answer should be an equation involving (at least)
these...

There are two goods, Good 1 and Good 2, with positive prices
p1 and p2. A consumer has the utility
function U(x1, x2) = min{2x1,
5x2}, where “min” is the minimum function, and
x1 and x2 are the amounts she consumes of
Good 1 and Good 2. Her income is M > 0.
(a) What condition must be true of x1 and
x2, in any utility-maximising bundle the consumer
chooses? Your answer should be an equation involving (at least)
these...

1. Consider the general form of the utility for goods that are
perfect complements.
a) Why won’t our equations for finding an interior solution to the
consumer’s problem work for this kind of utility? Draw(but do not
submit) a picture and explain why (4, 16) is the utility maximizing
point if the utility is U(x, y) = min(2x, y/2), the income is $52,
the price of x is $5 and the price of y is $2. From this picture
and...

Suppose u=u(C,L)=4/5 ln(C)+1/5 ln(L), where C = consumption
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of $W. The government collects tax on wage income at the marginal
rate of t%. The nominal price of consumption goods is $P. Further
assume that the consumer-worker is endowed with $a of cash
gift.
a) Write down the consumer-worker's budget constraint.
b) Write down...

A person's utility fromm goods A and B is U(A,B)= A x B. The
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goods equals $1.
a) Write the equation for the budget line and sketch it on a
graph – identifying relevant intercepts and slope – placing good A
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b) Find the quantities of A and B that maximize...

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