ANSWER ALL QUESTIONS AND SHOW YOUR WORK
Good review if it is accurate and fully answered!
QUESTION 8
Consider a Solow growth model where n=0, s=0.2, d=0.1, and F(K,N)=K^0.3*N^0.7. Suppose that initially at time t=0 the total factor productiviy is z=1 and the economy is in a steady state.
What is steady state investment per capita?
10 points
QUESTION 9
Consider a Solow growth model where n=0, s=0.2, d=0.1, and F(K,N)=K^0.3*N^0.7. Suppose that initially at time t=0 the total factor productiviy is z=1 and the economy is in a steady state.
What is the steady state growth rate of output per capita?
10 points
QUESTION 10
Consider the following Solow growth model. F(K,N)=K^0.5*N^0.5, with d=0.1, s=0.2, n=0.01, and z=1.
What is the steady state capital stock per worker?
10 points
QUESTION 11
Consider the following Solow growth model. F(K,N)=K^0.5*N^0.5, with d=0.1, s=0.2, n=0.01, and z=1.
What is income per capita in the steady state?
Suppose a representative consumer has preference over consumption (c) and leisure (1). His indifference curve is described by the following function: u(c, I) = 3 In(c) + 2 In(!). His endowment over time is given by h = 1. His wage rate is 2 in terms of consumption goods. Suppose he has 2 units of dividend income from firm and 1 unit of lump-sum tax from the government. (2) Compute this consumer's optimal choice over consumption, leisure and working time. (15 points) Suppose a representative consumer has preference over consumption (c) and leisure (). His indif- ference curve is described by the following function: u(c, l) = 31n(c) + 21n(1). His endowment over time is given by h = 1. His wage rate is 2 in terms of consumption goods. Suppose he has 2 units of dividend income from firm and 1 unit of lump-sum tax from the govern- ment. (2) Compute this consumer's optimal choice over consumption, leisure and working time. (15 points) (3) Now suppose there is an increase in the lump sum tax. Diagram the effects on consumer's optimal consumption and labor supply. Explain your results. (15 points) Note: under the above utility function, du/al MRSl,c= du/ac (3) Now suppose there is an increase in the lump sum tax. Diagram the effects on consumer's optimal consumption and labor supply. Explain your results. (15 points) Note: under the above utility function, MRSI,c = au/81 au/acSuppose a representative consumer has preferenee mmr consumption {e} and leisure (1]. Her indif ference curve is described by the following function: u= 2e+ where u is the utility level. Note that leisure and consumption goods are perfect substitutes under this preference. Her endowment over time is given by h =1. Her wage rate is 2 in terms ofoonsurnption goods. Suppose he has 2 units of dividend brooms from rm and 1 unit of lump tea: from the gmemment. (1} Write down the budget constraint for this consumer. [It] points} [2} Graph the budget constraint with leisure on the xaxis and consumption on the :raxis. Label the x and 3r intersections. What's the slope of the budget constraint? What's the economic meaning of this slope? [15 points) (3} Plot three indierenoe curves when the utility level is u = 1, 2.3 respectively. [Put them on the same graph of the budget constraint}. What are the slopw of these three indilferenoe curves\"? What's the economic meaning of these slopes? [15 points} (4] 1il'li'hat's the consumer's optimal choice over consumption and leisure? [15 points] [5] Under this preference, is more preferred to 1%? Does this preference satisfy the diminishing rate of substitution property? [15 points) Suppose a representative consumer has preference over consumption {c} and leisure {l}. Her indifference curve is described by the following function: LI = 2c + l where u is the utility level. Note that leisure and consumption goods are perfect substitutes under this preference
