1. Consider the following one-period model with a representative consumer, a representative firm and a government. Representative consumer's problem is given by: max In(c) + In(1) subject to : c= (1- t)ļw(h- 1) + ]. where c, I, w and z have their usual definition. The consumer has h units of time for working or consuming it as leisure. The government imposes a proportional tar of t on income as shown in the budget constraint for the representative consumer to finance government expenditure of G. The representative firm's problem is given by: max K"N- wNa (a) Define the competitive equilibrium for this economy. (b) Derive the first order conditions for the consumer's and firm's maximization problems.
1. Consider the following one-period model with a representative consumer, a representative firm and a government. Representative consumer's problem is given by: max In(c) + In(1) subject to : c= (1- t)ļw(h- 1) + ]. where c, I, w and z have their usual definition. The consumer has h units of time for working or consuming it as leisure. The government imposes a proportional tar of t on income as shown in the budget constraint for the representative consumer to finance government expenditure of G. The representative firm's problem is given by: max K"N- wNa (a) Define the competitive equilibrium for this economy. (b) Derive the first order conditions for the consumer's and firm's maximization problems.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![1. Consider the following one-period model with a representative consumer, a representative firm
and a government. Representative consumer's problem is given by:
max In(c) + In(1)
subject to : c= (1– t)[w(h- 1)+ #).
where e, I, w and a have their usual definition. The consumer has h units of time for working
or consuming it as leisure. The government imposes a proportional tar of t on income as shown
in the budget constraint for the representative consumer to finance government expenditure
of G. The representative firm's problem is given by:
max K" Na - wNa
(a) Define the competitive equilibrium for this economy.
(b) Derive the first order conditions for the consumer's and firm's maximization problems.
(c) Show that the production possibility frontier is given by e (1-t)K (h-1)-a.
(d) Using a diagram that describes the competitive equilibrium of the one-period model,
determine the effect of a decrease in t on equilibrium output, employment, wages and
profits. Explain your results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff90451e8-a668-460b-abc5-d967ff609c36%2F28a0e940-ab4b-45c5-9b3c-552235ad81d5%2F8na7b1m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the following one-period model with a representative consumer, a representative firm
and a government. Representative consumer's problem is given by:
max In(c) + In(1)
subject to : c= (1– t)[w(h- 1)+ #).
where e, I, w and a have their usual definition. The consumer has h units of time for working
or consuming it as leisure. The government imposes a proportional tar of t on income as shown
in the budget constraint for the representative consumer to finance government expenditure
of G. The representative firm's problem is given by:
max K" Na - wNa
(a) Define the competitive equilibrium for this economy.
(b) Derive the first order conditions for the consumer's and firm's maximization problems.
(c) Show that the production possibility frontier is given by e (1-t)K (h-1)-a.
(d) Using a diagram that describes the competitive equilibrium of the one-period model,
determine the effect of a decrease in t on equilibrium output, employment, wages and
profits. Explain your results.
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