Please answer the question fully and completely else I will rate negative, thanks! Question 3 Consider an economy with two consumers, A and B, two goods called 1 and 2 and one firm. Consumers A and B are each endowed with a unit of each good. The utility functions of each consumer are: A: 13 4 4 u (x₁‚x2 ) = lnx₁ + Inx2 B:u ₁₂ (x, ‚ x 2 ) = x, x 2 The firm B 1 A 1 1 2 produces good 2 using good 1 as an input, according to the production function f(y) = y where y is the quantity of good 1. Consumer A is the sole shareholder of the firm and the firm operates to maximize profit. Page 2 If P₁ and P2 determine the utility maximizing demand of consumer are the per unit prices of goods 1 and 2, . B for each good as a function of p, and P2 · If P₁ P 2 1 and are the per unit prices of goods 1 and 2, determine the profit maximizing demand of the firm for good 1 as a function of p₁ and p2. Ifp, and p2 are the per unit 1 prices of goods 1 and 2, determine the utility maximizing demand of consumer A for each good as a function of p₁ and P2. Treat good 1 as the numeraire and set P₁ 1 = 1. Determine the value of p2 the market, i. e., supply equals demand. which clears Question 3 Consider an economy with two consumers, A and B, two goods called 1 and 2 and one firm. Consumers A and B are each endowed with (1/2) a unit of each good. The utility functions of each consumer are: A uA(x1, x2) = ln x₁ + ln x2 B: UB(x1, x2) = x/4x3/4 The firm produces good 2 using good 1 as an input, according to the production function f(y) = √√√y where y is the quantity of good 1. Consumer A is the sole shareholder of the firm and the firm operates to maximize profit. Page 2 1. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the utility maximizing demand of consumer B for each good as a function of p₁ and p2. 2. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the profit maximizing demand of the firm for good 1 as a function of p₁ and p2. 3. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the utility maximizing demand of consumer A for each good as a function of p1 and p2. Treat good 1 as the numeraire and set p₁ = 1. Determine the value of p2 which clears the market, i.e., supply equals demand.
Please answer the question fully and completely else I will rate negative, thanks! Question 3 Consider an economy with two consumers, A and B, two goods called 1 and 2 and one firm. Consumers A and B are each endowed with a unit of each good. The utility functions of each consumer are: A: 13 4 4 u (x₁‚x2 ) = lnx₁ + Inx2 B:u ₁₂ (x, ‚ x 2 ) = x, x 2 The firm B 1 A 1 1 2 produces good 2 using good 1 as an input, according to the production function f(y) = y where y is the quantity of good 1. Consumer A is the sole shareholder of the firm and the firm operates to maximize profit. Page 2 If P₁ and P2 determine the utility maximizing demand of consumer are the per unit prices of goods 1 and 2, . B for each good as a function of p, and P2 · If P₁ P 2 1 and are the per unit prices of goods 1 and 2, determine the profit maximizing demand of the firm for good 1 as a function of p₁ and p2. Ifp, and p2 are the per unit 1 prices of goods 1 and 2, determine the utility maximizing demand of consumer A for each good as a function of p₁ and P2. Treat good 1 as the numeraire and set P₁ 1 = 1. Determine the value of p2 the market, i. e., supply equals demand. which clears Question 3 Consider an economy with two consumers, A and B, two goods called 1 and 2 and one firm. Consumers A and B are each endowed with (1/2) a unit of each good. The utility functions of each consumer are: A uA(x1, x2) = ln x₁ + ln x2 B: UB(x1, x2) = x/4x3/4 The firm produces good 2 using good 1 as an input, according to the production function f(y) = √√√y where y is the quantity of good 1. Consumer A is the sole shareholder of the firm and the firm operates to maximize profit. Page 2 1. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the utility maximizing demand of consumer B for each good as a function of p₁ and p2. 2. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the profit maximizing demand of the firm for good 1 as a function of p₁ and p2. 3. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the utility maximizing demand of consumer A for each good as a function of p1 and p2. Treat good 1 as the numeraire and set p₁ = 1. Determine the value of p2 which clears the market, i.e., supply equals demand.
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.1P
Related questions
Question
Transcribed Image Text:Please answer the question fully and completely else I
will rate negative, thanks! Question 3 Consider an
economy with two consumers, A and B, two goods
called 1 and 2 and one firm. Consumers A and B are
each endowed with a unit of each good. The utility
functions of each consumer are: A:
13
4 4
u (x₁‚x2 ) = lnx₁ + Inx2 B:u ₁₂ (x, ‚ x 2 ) = x, x 2
The firm
B 1
A
1
1 2
produces good 2 using good 1 as an input, according to
the production function f(y)
=
y where y is the quantity
of good 1. Consumer A is the sole shareholder of the
firm and the firm operates to maximize profit. Page 2 If
P₁
and P2
determine the utility maximizing demand of consumer
are the per unit prices of goods 1 and 2,
.
B for each good as a function of p, and P2 · If P₁
P 2
1
and
are the per unit prices of goods 1 and 2, determine
the profit maximizing demand of the firm for good 1 as
a function of p₁ and p2. Ifp, and p2 are the per unit
1
prices of goods 1 and 2, determine the utility
maximizing demand of consumer A for each good as a
function of p₁ and P2. Treat good 1 as the numeraire
and set P₁
1
= 1. Determine the value of p2
the market, i. e., supply equals demand.
which clears
Transcribed Image Text:Question 3
Consider an economy with two consumers, A and B, two goods called 1 and 2 and one firm.
Consumers A and B are each endowed with (1/2) a unit of each good. The utility functions of
each consumer are:
A uA(x1, x2) = ln x₁ + ln x2
B: UB(x1, x2) = x/4x3/4
The firm produces good 2 using good 1 as an input, according to the production function f(y) = √√√y
where y is the quantity of good 1. Consumer A is the sole shareholder of the firm and the firm
operates to maximize profit.
Page 2
1. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the utility maximizing
demand of consumer B for each good as a function of p₁ and p2.
2. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the profit maximizing demand
of the firm for good 1 as a function of p₁ and p2.
3. If p₁ and p2 are the per unit prices of goods 1 and 2, determine the utility maximizing
demand of consumer A for each good as a function of p1 and p2.
Treat good 1 as the numeraire and set p₁ = 1. Determine the value of p2 which clears the
market, i.e., supply equals demand.
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