Question

Questions 6 through 10 refer to an exchange economy consisting of two consumers: Agnieszka (A) and Bob (B), who consume two goods: bananas (x1) and motor oil (x2). Good 2 is the numeraire, with p2=1.

Q6 Agnieszka is endowed with ωA=(25,20). The equation for her budget constraint is:

a. p1x1A+x2A=25+20p1

b. p1x1A+x2A=25p1

c. p1x1A+x2A=25p1+20

d. p1x1A+x2A=45.

e.

Q7. Bob’s utility function is uB(x1B,x2B)=x1B(x2B)2. This implies that:

a. The market value of his gross demand for x1 is half that of his gross demand for x2

b. He will spend two-thirds of the market value of his endowment on x1

c. We can’t say anything about his demand behaviour without knowing his endowment.

d. He will only consume x1 if it is less than twice as expensive as x2

e. He will always consume twice as many units of x2 as he does of

Q8. Agnieszka is endowed with ωA=(25,20), and her utility function is uA(x1A,x2A)=(x1A)2x2A. Her demand function for x₁ is:

a. x1A=23(25p1+20p1).

b.x1A=13(25p1+20p1).

c. x1A=13(25+20p1).

d. x1A=23(25p1+20).

e.

Q9. Agnieszka is endowed with ωA=(25,20), and her demand for x₂ isx2A=13(25p1+20). Bob is endowed with  ωB=(25,10), and his demand for x₂ is x2B=23(25p1+10). In competitive equilibrium, the price of x₁ will be:

a. p1=23

b. p1=2215

c. p1=32

d. p1=1

e.

Q10 At a competitive equilibrium allocation of this economy:

a. It is not possible to make Agnieszka better off without making Bob worse off.

b. The indifference curves enclose a "lens-shaped" region of potential Pareto improvements.

c. The set of allocations preferred by Agnieszka overlaps with the ones preferred by Bob.

d. Both Agnieszka and Bob must have the same utility.

e. It is necessary to redistribute some of Bob’s endowments by giving them to Agnieszka.

Thank you!!!

Answer 1

Answer 6

Agnieszka (A) and Bob (B), who consume two goods: bananas (x₁) and motor oil (x₂). Good 2 is the numeraire, with p₂=1.

Agnieszka is endowed with ω_A=(25,20).

Thus, the equation for her budget constraint is

p₁x_1A + p₂x_2A = 25p₁ + 20p₂

or, p₁x_1A + x_2A = 25p₁ + 20 .......(since p₂=1)

Thus, the correct option is (c).

Answer 7

We know, if the utility function is of the form U(x,y) = x^ay^b, then the corresponding demand functions can be derived as:

when m is the income.

Now, Bob’s utility function is u_B(x_1B,x_2B)=x_1B(x_2B)²

The demand functions in this case are as follows, where m is the income or the market value of Bob's endowment:

Hence, clearly, the market value of his gross demand for x₁ is half that of his gross demand for x₂.

Thus, the correct option is (a).

Answer 8

Agnieszka is endowed with ω_A=(25,20), and her utility function is u_A(x_1A,x_2A)=(x_1A)²x_2A

We know, the equation for her budget constraint is p₁x_1A + x_2A = 25p₁ + 20

Her demand function for x₁ is

Thus, the correct option is (d).

Answer 9

Agnieszka is endowed with ω_A=(25,20), and her demand for x₂ is x_2A=(25p1+20)/3. Bob is endowed with ω_B=(25,10), and his demand for x₂ is x_2B=2(25p₁+10)/3.

Now, x_2A + x_2B = ω_2A + ω_2B = (20 + 10) = 30

In competitive equilibrium, the price of x₁ will be 2/3.

Thus, the correct option is (a).

Answer 10

From the Fist Welfare Theorem, when there is a perfectly competitive equilibrium, the allocation of resources will be Pareto Optiomal.

Thus, at a competitive equilibrium allocation of this economy, it is not possible to make Agnieszka better off without making Bob worse off.

Thus, the correct option is (a).