Question

- Olivia likes to eat both apples and bananas. At the grocery store, each apple costs $0.20 and each banana cost $0.25. Olivia’s utility function for apples and bananas is given by U(A, B) = 6 (AB)1/2 . If Olivia has $4 to spend on apples and bananas, how many of each should she buy to maximize her satisfaction?

Use the tangency condition to find the optimal amount of A to relative to B .

MUA/PA = MUB/PB

Now plug this into the budget constraint to find the optimal amount of B to purchase.

Finally, plug this result into the relationship between A and B above (that we found using the tangency condition) to determine the optimal amount of A ; A =1.25(8) =10 .

Therefore, she should buy 10 apples and 8 bananas to maximize her utility.

- A consumer purchases two goods, food (F) and clothing (C) . Her utility function is given by

U(F,C) = FC + F . The price of food is PF , the price of clothing is PC , and the consumer’s income is I.

a) What is the equation for the demand curve for clothing?

b) Is clothing a normal or inferior good in this case?

Setting up the tangency condition implies

Substituting this result into the budget line implies

Since the amount of clothing purchased will increase as income increases, as noted by the

demand curve, clothing is a normal good, and not an inferior good

3. Consider the following information:

- Jessica’s utility function is
*U*(*x*,*y*) =*xy*. - Maria’s utility function is
*U*(*x*,*y*) = 1,000*xy*. - Nancy’s utility function is
*U(x,y) =*-*xy*. - Chawki’s utility function is
*U(x,y) = xy*- 10,000. - Marwan’s utility function is
*U(x,y)= x*(*y*+ 1).

Which of these persons have the same preferences as Jessica?

- Suppose the market demand for a product is given by

*Q ^{d}* = 1000 −10

and the market supply is given by

*Q ^{s}=* −50 + 25

- What are the equilibrium price and quantity?
- Calculate the Consumer Surplus.
- At the market equilibrium, what is the price elasticity of demand? Is demand elastic, unitary elastic or inelastic?
- Suppose the price in this market is $25. What is the amount of excess demand?

- The following conversation was heard among four economists discussing whether the minimum wage should be increased:

Economist A. “Increasing the minimum wage would reduce unemployment of minority teenagers.”

Economist B. “Increasing the minimum wage would present an unwarranted interference with private relations between workers and their employers.”

Economist C. “Increasing the minimum wage would raise the incomes of some unskilled workers.”

Economist D. “Increasing the minimum wage would benefit higher-wage workers and would probably be supported by organized labor.”

Which of these economists are using positive analysis and which are using normative analysis in arriving at their conclusions? Which of these predictions might be tested with empirical data? How might such tests be conducted?

5. If production function is given by Q = KL, what would happen when both inputs double.

6. The production function is given by Q =
K^{1/3}L^{2},

a. Determine the marginal product of capital,
MP_{k}?

b. Does the law of diminishing marginal productivity apply for capital use?

7. Suppose MP_{L} = 20 and MP_{K} = 40 and the
rental rate on capital is $10. If the level of production is
currently efficient, what should the wage rate be?

Answer #1

The price of apple Pa= $0.20

The price of banana. Pb= $0.25

The budget of the consumer= $4

The budget constraint becomes:

0.20A+0.25B= 4

The utility function is:

U= 6AB/2= 3AB

The marginal utility of A, MUa

The marginal utility of B. MUb,

From the optimality condition:

MUA/PA = MUB/PB

3B/0.20= 3A/0.25

A/B= 0.25/0.20= 5/4

A=5B/4

Putting this value in the budget constraint,

0.20A+0.25B= 4

0.20(5B/4) +0.25B= 4

0.5B= 4

B= 8

, Thus, A= 5*8/4= 10

Angela's fruit options at the convenience store are apples and
bananas. Angela's utility function over apples, A, and bananas, B,
is given by: U(A,B)=A+B a. Describe Angela's preferences over
apples and bananas and explain her optimal decision rule b. What is
the optimal bundle if price of apples is $1 a pound and the price
of bananas is $2 a pound, and she has $100 a month to spend on
apples and bananas. c. This convenience store is closing for...

1. Consider the following information:
Jessica’s utility function is U(x,
y) = xy.
Maria’s utility function is U(x, y)
= 1,000xy.
Nancy’s utility function is U(x,y) =
-xy.
Chawki’s utility function is U(x,y) = xy -
10,000.
Marwan’s utility function is U(x,y)= x(y +
1).
Which of these persons have the same preferences as Jessica?
2. Suppose the market demand for a product is given by
Qd = 1000 −10P
and the market supply is given by
Qs= −50...

Evelyn eats only apples and bananas. Suppose Evelyn has the
following utility function: ?(??, ??) = ????.
a. Evelyn currently has 40 apples and 5 bananas. What is
Evelyn’s utility at this bundle? Graph the indifference curve
showing all bundles that Evelyn likes exactly as well as the bundle
(40, 5).
b. Norah offers to trade Evelyn 15 bananas if she will give her
25 apples. Would Evelyn take this trade? Explain.
c. What is the largest number of apples...

utility function u(x,y) = x3 ·y2
I am going to walk you through the process of deriving the
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happiest. To do this, we are going to apply what we learnt about
derivatives.
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amount since you would not be able to aﬀord it. Suppose the price
of a single apple is Px = 2 while the price of...

Dan’s preferences are such that left shoes (good x) and right
shoes (good y) are perfect complements. Specifically, his
preferences are represented by the utility function U (x, y) =
minimum{x, y}.
(a) Draw several of Dan’s indifference curves. Which bundles are
at the “kink- points” of these curves?
(b) Assume that Dan’s budget for shoes is M = 10 and that the
price of a right shoe is py = 2. Find and draw Dan’s demand curve
for left...

Santi derives utility from the hours of leisure (l) and from the
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needs to allocate the 24 hours in the day between leisure hours (l)
and work hours (h). Santi has a Cobb-Douglas utility function, u(c,
l) = c 2/3 l 1/3 . Assume that all hours not spent working are
leisure hours, i.e, h + l = 24. The price of a good is equal to 1...

Santi derives utility from the hours of leisure (l) and from the
amount of goods (c) he consumes. In order to maximize utility, he
needs to allocate the 24 hours in the day between leisure hours (l)
and work hours (h). Santi has a Cobb-Douglas utility function,
u(c,l) = c2/3l1/3. Assume that all hours not spent working are
leisure hours, i.e, h + l = 24. The price of a good is equal to 1
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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...

(1) Explain why the assumption of convex preferences
implies that “averages are preferred to extremes.” Make both a
formal argument and an intuitive one (that is, an explanation that
can be understood by the “man on the street.”)
(2) What does the negative slope of an indifference
curve imply about a consumer’s tastes for the two goods? How would
this change if one of the goods wasn’t a “good” at all (but instead
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