Consider an economy in which two commodities doors (Qi) and beds (Q2) are produced. The utility function of all consumers in the economy is given as U= qq,. The production functions for the production of doors and beds are given as q 4,-V, where x, is the input used in the production of doors and x2 is input used in producing beds. A and 92 (a) Determine the margina! rate of subsiitution (MRS) for all consumers in the economy. (3 marks) (b) Suppose x, +x, = 108, derive the Marginal Rate of Transformation (MRT) for this economy. (c) Compute the quantity of doors and beds produced and sold at which the entire economy attains equilibrium. (7 marks) (3 marks)

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Consider an economy in which two commodities doors (Q) and beds (Q2) are produced. The
utility function of all consumers in the economy is given as U = q q, . The production
functions for the production of doors and beds are given as q
x,
3
1
and 92
where x, is the input used in the production of doors and x2 is input used in producing beds.
(a) Determine the margina! rate of subsiitution (MRS) for all consumers in the economy.
(3marks)
(b) Suppose x, +x, 108, derive the Marginal Rate of Transformation (MRT) for this
economy.
(c) Compute the quantity of doors and beds produced and sold at which the entire
economy attains equilibrium.
(d) What is the equilibrium price of a unit of door and a unit of bed in the economy?
(7 marks)
(3 marks)
(2marks)
Transcribed Image Text:Consider an economy in which two commodities doors (Q) and beds (Q2) are produced. The utility function of all consumers in the economy is given as U = q q, . The production functions for the production of doors and beds are given as q x, 3 1 and 92 where x, is the input used in the production of doors and x2 is input used in producing beds. (a) Determine the margina! rate of subsiitution (MRS) for all consumers in the economy. (3marks) (b) Suppose x, +x, 108, derive the Marginal Rate of Transformation (MRT) for this economy. (c) Compute the quantity of doors and beds produced and sold at which the entire economy attains equilibrium. (d) What is the equilibrium price of a unit of door and a unit of bed in the economy? (7 marks) (3 marks) (2marks)
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