## Econ

### 1 Question 1: The OLG model with elastic labor and govern-ment  加拿大经济学assignment代写

We now consider an overlapping generations model in which households value both consumption good and leisure. The preference is given by

where, lj is leisure and K is a parameter governing flow of utility from leisure. For simplicity,we also assume that when households are retired leisure is not a choice variable any more. The household budget constraints are given by

cj+sj = (1-lj)hjw+(1+r)sj-1,j=1,2,

cj+sj = (1+r)sj-1, j=3, 4,

where, (1 – lj)hzw is labor income, (1 +r)sj-1 is investment income, and s0= 0.

#### a) Assume that h1= 1,h2= 1.5,β=0.98,σ=2,k=3, A= 1,α= 0.36 and δ = 0.05. Solve the model using the Gauss Seidel algorithm.

b) Find the value of β to match anmual interest rate of 4%. Report graphs of consumption,government collects social security taxes (TSS) from the current working generations to pay social security benefits of the current retiring generations. We let Pensj =ΨwH denote social security benefits, where亚is a replacement rate and wH is average labor income. The household budget constraints are given by

cj+sj = (1-τss)(1-lj)hjw+(1 +r)sj-1 ,j=1 and 2,

cj+sj = (1+r)sj-1 + Pensj, j= 3 and 4,

where, (1 – lj)hjw is labor income, (1 + r) sj-1 is investment income, and s0= 0.

The government budget constraint is balanced each period

Note that, we assume that social security tax rate (τss) adjusts to balance the government budget.

Assume that h1 = 1, h2= 15,β =0.98,σ =2, K= 3,A=1, a= 0.36, δ = 0.05 and ψ= 0.4. Solve the model using the Gauss Seide! algorithm.

d) Now, consider a social security reform in which the government cuts generosity of the social security system by reducing the replacement rate to Ψ= 0.2. Determine the effects on the market wage and interest rates, and on aggregate capital, labor and output. Report the life-cycle profiles of consumption, savings, labor supply and labor earnings before and after the reform. Discuss the results.

### 2 Question 2: The Neoclassical growth model with elast ic labor and government

We consider a closed economy model illed with a representative household, a representative firm and a government. Time is discrete (t=0, 1, …).

[1] The representative household lives infinitely and has the following preference:

where β is the time discount factor, ct is cosumption,lt is lesure andThe agent is given capital ko initially and one unit of time in each period. The agent can invest in capital market. The labor supply is nt = 1 – l1. The houshold lifet ime budget constraint is

where q and it are consumption and investment; rt is rental rate; and wt is wage rate;τctktandτnt are taxes on consumption, capital income and labor income, respectively. The law of motion for capital is

ky+1=(1-δ)kt+it,

where capital depreciates at a constant rate δ.

[2] There is a representative firm which has access to the fllowing CRS technology:

where, At is the total factor productivity, kt is capital input and nt is labor input. The representative firmm rents inputs in competitive markets.  加拿大经济学assignment代写

#### [3] The government collects tax renenues to finance an investment subsidy program and a sequence of government purchases. The government lifetime budget constraint is given by

a) Assume that β= 0.98,σ=2,θ=2,ψ=2,A=1,a=0.36, δ= 0.05,τc= 0.05,τk=0.25, and τn= 0.20. Find the steady state solution using Dynare.

b) Start from the steady state in (a) and assume that there will be a decrease in TFP for 10 periods ahead, At+10 = 0.95. Detemine the dynamic ffects of such TFP shock on macroeconomic aggregates and prices, incuding capital, labor supply, output, the wage and interest rates. Explain the undedying mechanism.  加拿大经济学assignment代写

c) Start from the steady state in (c) and assume that the government cuts labor income tax rate to 15% forever. Detemine the dynamic effects of the tax cut on the economy, includ-ing capital, labor supply, output, the wage and interest rates. Explain the undedying mochanism.

d) Assume that the government cuts capital income tax from 25% to 20% immediately in response to the negative TFP shock in (b). Detemine the effects of the on the economy.Are there any difences in macroeconomic variables when comparing to (b)? Why?

### 3 Question 3: Taxes and consumption-saving  加拿大经济学assignment代写

Consider a simple model of endowment eoonomy flled with a mass of infinitely lived agents.At begining of each time period, agents are endowed an amount of income yt, which follows a stochastic process that has two states: low and high, .The preference has a form of , where, β∈(0,1) and ct is consumption at time t. There are no insurance

markets available. However, agents can either save or borrow to a certain limit (b). The market interest rateis 1 +r. The capital income tax rate is τt.

#### An agent chooses consumption (c) and bond holdings (b+1) to solve his/her utility max-imization problem according to

Assume the following parameter values

a) Consider a partial equilibrium economy in which the market interest is constant at 3%.Solve the household problem numerically, using value function iteration. Obtain the household’s decision rules and value functions, and simulate the distribution of agents.

b) Consider a partial equilibrium economy as in a). Remove the capital income tax (τ r= 0)and report the effects on the decision rules and value functions.

c) Construct a measure of wealth inequality (Gini cofficient) and show the ffects on wealth inequality when moving from a) to b).