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t Suppose that in the basic one- period model, there is no government spending and no...
4. (20 points) Suppose that, in the basic one-period model, there is no government spending and...
4. (20 points) Suppose that, in the basic one-period model, there is no government spending and no taxes. Production by the representative firm produces pollution in proportion to the amount of output produced. Given any consumption bundle (a consumption-leisure pair), the consumer is worse of the more pollution there is. a. In a diagram, show the competitive equilibrium and the Pareto optimum. Show that the competitive equilibrium is not Pareto optimal, and explain why. Is more or less output produced...
1. (45 points) Consider the closed-economy one-period macroeconomic model developed in class. The...
1. (45 points) Consider the closed-economy one-period macroeconomic model developed in class. The consumer is endowed with h units of time, and chooses consumption C and leisure ` to maximize U = log(C) + θlog(`), subject to the budget constraint C = wNs + π. Production is described by Y = zNd . Government spending G is financed with a proportional revenue tax (tax rate τ ) on the firm. (a) (10) Find the firm’s optimal demand for labor Nd...
2 Calculating a Pareto optimal allocation Suppose the representative household has the following utility function: U...
2 Calculating a Pareto optimal allocation Suppose the representative household has the following utility function: U (C,) InC +0.5ln l where C is consumption and 1 is leisure. The household's time constraint is I+N-1 where Ns is the representative household's labour supply. Further assume that the production function is Cobb-Douglas 0.5 0.5 where 2-1 and K = 1 2.1 Assuming that the government spending is G = 0, use the Social Planners problem to solve for Pareto optimal numerical values...
Suppose the representative household has the following utility function: U (C; l) = ln C +...
Suppose the representative household has the following utility function: U (C; l) = ln C + 0:5 ln l where C is consumption and l is leisure. The householdís time constraint is l+N=1 where Ns is the representative householdís labour supply. Further assume that the production function is Cobb-Douglas zK0:5 (N)0:5 where z = 1 and K = 1: 2.1 Assuming that the government spending is G = 0; use the Social Plannerís problem to solve for Pareto optimal numerical...
Consider the two-period model from Chapter 9, and assume there is one representative consumer with utility...
Consider the two-period model from Chapter 9, and assume there is one representative consumer with utility function uc,d) = Iníc) + In(d), so the time discount factor is 3 = 1. There is also a government that levies lump-sum taxes in the current and future periods. The government has expenditures of G = 580 in the current period and G' = 630 in the future period. (a) Suppose the consumer has current and future income (w.y') = (3500, 6510), and...
2. (25 points). Suppose that government spending makes private firms more productive, e.g., spending on roads and bridg...
2. (25 points). Suppose that government spending makes private firms more productive, e.g., spending on roads and bridges might reduce transport costs. (a) Using the production possibilities graph described in chpt. 5 of the text and in Lecture 5, show how an increase productive government spending could increase household welfare (b) Show that the equilibrium effects on consumption and hours worked are ambigu- ous, but but that output definitely increases. Hint: Consider the induced income and substitution effects.
2. (25...
2. For the closed-economy, one-period model, suppose that U(C,) = min(C,Bl. and F(K, N) 0K+5N, where...
2. For the closed-economy, one-period model, suppose that U(C,) = min(C,Bl. and F(K, N) 0K+5N, where β > 0, α > 0, and δ > 0, Determine con- sumption, employment, output, leisure, and the real wage in a competitive equi- librium, and explain your solutions. Also draw a diagram with the consumers preferences and the production possibilities frontier, and show the competitive equilibrium in this diagram.
3 Exercise 3 - Basic OLG model Consider the following two-period OLG model. People consume in...
3 Exercise 3 - Basic OLG model Consider the following two-period OLG model. People consume in both periods but work only in period two. The inter-temporal utility of the representative individual in the first period is where c and c2 are consumption and kı (which is given) and k2 are the stocks of capital in periods one and two. ns is work and is government expenditure in period two which is funded by a lump-sum tax in period two, T2....
Alter the Diamond-Dybvig model in the following way. Suppose that there are two assets, an illiquid...
Alter the Diamond-Dybvig model in the following way. Suppose that there are two assets, an illiquid asset that returns 1+r units of consumption goods in period 2 for each unit invested in period 0, and a liquid asset that returns one unit of consumption goods in period 1 for each unit invested in period 0. The illiquid asset production technology cannot be interrupted in period 1. The model is otherwise the same as in class. a. Determine a consumers lifetime...
Question 2 A. Suppose that the aggregate demand and supply curve for solar panels is given...
Question 2 A. Suppose that the aggregate demand and supply curve for solar panels is given by P = 10 - 2Q and P = 1 + 5Q respectively. i. Draw the demand and supply curves for solar panels for this market and mark the equilibrium. Label this point as A. ii. Calculate the consumer surplus, producer surplus and total economic surplus of the market when it is in equilibrium. B. Suppose that, following a technological advancement, solar panels can...
4. (20 points) Suppose that, in the basic one-period model, there is no government spending and no taxes. Production by the representative firm produces pollution in proportion to the amount of output produced. Given any consumption bundle (a consumption-leisure pair), the consumer is worse of the more pollution there is. a. In a diagram, show the competitive equilibrium and the Pareto optimum. Show that the competitive equilibrium is not Pareto optimal, and explain why. Is more or less output produced...
2 Calculating a Pareto optimal allocation Suppose the representative household has the following utility function: U (C,) InC +0.5ln l where C is consumption and 1 is leisure. The household's time constraint is I+N-1 where Ns is the representative household's labour supply. Further assume that the production function is Cobb-Douglas 0.5 0.5 where 2-1 and K = 1 2.1 Assuming that the government spending is G = 0, use the Social Planners problem to solve for Pareto optimal numerical values...
Consider the two-period model from Chapter 9, and assume there is one representative consumer with utility function uc,d) = Iníc) + In(d), so the time discount factor is 3 = 1. There is also a government that levies lump-sum taxes in the current and future periods. The government has expenditures of G = 580 in the current period and G' = 630 in the future period. (a) Suppose the consumer has current and future income (w.y') = (3500, 6510), and...
2. (25 points). Suppose that government spending makes private firms more productive, e.g., spending on roads and bridges might reduce transport costs. (a) Using the production possibilities graph described in chpt. 5 of the text and in Lecture 5, show how an increase productive government spending could increase household welfare (b) Show that the equilibrium effects on consumption and hours worked are ambigu- ous, but but that output definitely increases. Hint: Consider the induced income and substitution effects.
2. (25...
2. For the closed-economy, one-period model, suppose that U(C,) = min(C,Bl. and F(K, N) 0K+5N, where β > 0, α > 0, and δ > 0, Determine con- sumption, employment, output, leisure, and the real wage in a competitive equi- librium, and explain your solutions. Also draw a diagram with the consumers preferences and the production possibilities frontier, and show the competitive equilibrium in this diagram.
3 Exercise 3 - Basic OLG model Consider the following two-period OLG model. People consume in both periods but work only in period two. The inter-temporal utility of the representative individual in the first period is where c and c2 are consumption and kı (which is given) and k2 are the stocks of capital in periods one and two. ns is work and is government expenditure in period two which is funded by a lump-sum tax in period two, T2....
Alter the Diamond-Dybvig model in the following way. Suppose that there are two assets, an illiquid asset that returns 1+r units of consumption goods in period 2 for each unit invested in period 0, and a liquid asset that returns one unit of consumption goods in period 1 for each unit invested in period 0. The illiquid asset production technology cannot be interrupted in period 1. The model is otherwise the same as in class. a. Determine a consumers lifetime...
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