闪电代写 -代写CS作业_CS代写_Finance代写_Economic代写_Statistics代写_代码代做_IT代写_加急帮助

Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Economics 320: Macroeconomic Theory II

Assignment Three

Part 1: (50 points)

This question examines government spending ﬁnanced by lump-sum taxes. There is a single representative household which has h = 10 units of time which it can divide between working and leisure. The household’s preferences over consumption of the ﬁnal good, C, leisure, l, and government spending, G, are given by the following utility function:

U(C, l) + λV(G) = 3ln(C + a) + 2ln(l) + λG0.2

where λ is a constant to be speciﬁed below. For this question assume that a = 4.

Production of the ﬁnal good uses labour only with technology

Y = zND ,

where z ﬂuctuates randomly between a relatively low level of zL = 15 and a relatively high level of zH = 20.

The government ﬁnances government spending by lump-sum taxes equal to T = G imposed on the household. In periods in which productivity is high, the government does not spend or tax, G = T = 0. But in periods when productivity is low, the govern- ment spends and taxes whatever amount it takes to keep output at the same level as it is when productivity is high. That is, the government uses government spending and tax- ation to eliminate ﬂuctuations in output.

A) (15 points) Determine the equilibrium levels of household consumption, leisure, labour hours, output, government spending, the tax level, and the real wage for the two types of periods (that is, periods in which productivity is low and government spending is positive and periods in which productivity is high and government spending is zero).

B) (10 points) Suppose that λ = 1. 0. Determine whether or not the government’s policy of spending and taxing to maintain a constant level of output is a good one if the government’s objective is to maximize household utility. You should justify your answer by calculating household utility when z is low and G = 0 and calculating household utility when z is low and G equals the value you calculated in (1.A) and comparing the two utility levels. Provide economic intuition for your ﬁnding.

C) (10 points) Suppose now that λ = 2. 0. Determine whether or not the government’s policy of spending and taxing to maintain a constant level of output is a good one if the government’s objective is to maximize household utility. Provide economic intu- ition for your ﬁnding.

D) (15 points) Calculate the level of λ up to the third decimal place (call it λ~ such that the household is just as well off when the government follows its stabilization policy as when it does not. Assuming that λ > λ~, explain why I make the following claim: “The welfare gains that the household experiences under this government policy do not really have anything to do with stabilizing output. ”

Part 2: (50 points)

Consider the Diamond and Dybvig model we studied in Topic 7:

Suppose there are N = 100 households with utility U(C) = 1 − e−C endowed with one unit of the conumption good in T = 0, and the proportion which will be impatient and want to consume in T = 1 is λ = 0. 4. The remaining households want to constume in

T = 2.

There are three assets/technologies in which the household can put its endowment:

1. A storage technology which simply carries the unit of consumption forward one period with no loss or gain.

2. An investment opportunity which gives the investor r1 = 1 if liquidated early, and r2 = 3 if held to maturity in T = 2.

3. A deposit agreement offered by a bank which gives the depositor r 1(d) = 1. 124 if with- drawn in T = 1, and r 2(d) = 2. 752 if withdrawn in T = 2.

A) (10 points) Show that the deposit agreement offered by the bank is viable (i.e. show that as long as the patient people wait until T = 2 to withdraw, the bank will not run out of money).

B) (30 points) For each of the three assets/technologies, calculate the measure of liquid- ity introduced in class, the expected return, and the expected utility. Fill in the table below: