a) Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by MRSM = 2yM/XM for Mohammed, MRSxy= 2yD/xp for David and MRSy = ys/xs for Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient? Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain. b) There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A's marginal rate of technical substitution of labour for capital is 4 while B's marginal rate of technical substitution of labour for capital is 2. Is the current production of the two firms efficient? If not, describe an exchange of inputs that would improve efficiency. Can these production levels of the two firms be observed in a perfectly competitive equilibrium of a production and exchange economy? Explain. c) State the first theorem of welfare economics of a production and exchange economy. Which conditions must be satisfied for the Pareto efficiency of an allocation of a production and exchange economy (assuming that all goods are used, produced and consumed in strictly positive quantities)? Discuss and explain.
a) Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by MRSM = 2yM/XM for Mohammed, MRSxy= 2yD/xp for David and MRSy = ys/xs for Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient? Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain. b) There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A's marginal rate of technical substitution of labour for capital is 4 while B's marginal rate of technical substitution of labour for capital is 2. Is the current production of the two firms efficient? If not, describe an exchange of inputs that would improve efficiency. Can these production levels of the two firms be observed in a perfectly competitive equilibrium of a production and exchange economy? Explain. c) State the first theorem of welfare economics of a production and exchange economy. Which conditions must be satisfied for the Pareto efficiency of an allocation of a production and exchange economy (assuming that all goods are used, produced and consumed in strictly positive quantities)? Discuss and explain.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.1P
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Only Answer PART (c)
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2yD/xD for David and MRSxy
=
a) Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are
two goods available, good x, and good y. The marginal rates of substitution (where good x is
on the horizontal axis and good y is on the vertical axis) are given by MRSM 2yM/XM for
Mohammed, MRSxy
Ys/xs for Mohammed and David are
both consuming twice as much of the good x than good y, while Susan is consuming equal
amounts of x and y. What are the conditions for Pareto efficiency in an exchange economy?
Are these consumption levels economically efficient? Can these consumption allocations be
observed in a perfectly competitive equilibrium in an exchange economy without production?
Explain.
=
b) There are two firms in the economy. Each firm employs positive amounts of capital and
labour. The technology satisfies diminishing marginal rate of technical substitution of labour
for capital. Currently, A's marginal rate of technical substitution of labour for capital is 4 while
B's marginal rate of technical substitution of labour for capital is 2. Is the current production of
the two firms efficient? If not, describe an exchange of inputs that would improve efficiency.
Can these production levels of the two firms be observed in a perfectly competitive equilibrium
of a production and exchange economy? Explain.
c) State the first theorem of welfare economics of a production and exchange economy. Which
conditions must be satisfied for the Pareto efficiency of an allocation of a production and
exchange economy (assuming that all goods are used, produced and consumed in strictly
positive quantities)? Discuss and explain.
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