Any help would be greatly appreciated Here is a question from a high level economics course Assume a two period Ramsey economy with consumers and producers Utility function and production function are U(c1,c2) log(c1) (1 (1 ))log(c2) and Y AK ()L (1) Assume 0 Also assume that the interest rate is r Denote by Rk the rate of remuneration of capital and w the rate of remuneration of labor Assume that the government levies the following taxes a on asset income, c on consumption, f on firm profits and l on labor The labor tax is paid by the firm There is no inheritance Which of these taxes are now part of the Euler Equation Derive the new Euler Equation Analyze this statement the taxes which are not part of the Euler Equation do not distort anything in the economy So far we have assumed that these taxes are just wasted Now let us assume that government spending isactually part oftheproduction function Y AK ()L ()G (1) Also, assumethatthe government runs a balanced budget and uses only one tax, which is levied on output (at rate per unit output) Also assume (0,1), (0,1), and 1 (a) Write down the government budget constraint if there is a balanced budget every period (b) Show that output is increasing ingovernment expenditure butatadecreasing rate Providean intuitive explanation of this property Do you think this is realistic Why or why not (c) Write down the firms profit maximization problem and obtain the FOC for K and L (Note that firms do not choose G) (d) Assume for the rest of the exercise that 0 (Note that x 0 1) Rewrite the FOC with respect to capital Use the government budget constraint to eliminate G from the FOC Then derive r as a function of , , A and (e) Derive the Euler equation and replace r with the expression found in 3(d) (f) What is the relationship between the growth rate in consumption and the tax rate Find the rate of taxation that maximizes consumption growth Provide a graphical representation of the growth rate of consumption as a function of the tax rate

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 24, 2024

Any help would be greatly appreciated!! Here is a question from a high-level economics course: Assume a two period Ramsey economy with consumers and producers.

Any help would be greatly appreciated!! Here is a question from a high-level economics course:

Assume a two period Ramsey economy with consumers and producers. Utility function and production function are:

U(c1,c2) = log(c1) + (1/(1 +))log(c2)

and Y=AK^()L^(1).

Assume >0. Also assume that the interest rate is r. Denote by Rk the rate of remuneration of capital and w the rate of remuneration of labor.

Assume that the government levies the following taxes: a on asset income, c on consumption, f on firm profits and l on labor.

The labor tax is paid by the firm.There is no inheritance.

Which of these taxes are now part of the Euler Equation? Derive the new Euler Equation.
Analyze this statement: the taxes which are not part of the Euler Equation do not distort anything in the economy.
So far we have assumed that these taxes are just wasted. Now let us assume that government spending isactually part oftheproduction function Y=AK^()L^()G^(1). Also, assumethatthe government runs a balanced budget and uses only one tax, which is levied on output (at rate per unit output). Also assume (0,1), (0,1), and + <1.

(a) Write down the government budget constraint if there is a balanced budget every period.

(b) Show that output is increasing ingovernment expenditure butatadecreasing rate. Providean intuitive explanation of this property.Do you think this is realistic?Why or why not?

(c) Write down the firms profit maximization problem and obtain the FOC for K and L. (Note that firms do not choose G).

(d) Assume for the rest of the exercise that = 0 (Note that x^0= 1). Rewrite the FOC with respect to capital.

Use the government budget constraint to eliminate G from the FOC. Then derive r as a function of , , A and .

(e) Derive the Euler equation and replace r with the expression found in 3(d).

(f) What is the relationship between the growth rate in consumption and the tax rate? Find * the rate of taxation that maximizes consumption growth. Provide a graphical representation of the growth rate of consumption as a function of the tax rate.