Macroeconomic Theory Report

Macroeconomics I

Fall 2015

Homework 1 

1. Consider the following modification of the simple IS-LM model        of the macroeconomy. Suppose that the demand for money depends on after-tax income, so that

M/P = L(r, Y – T).

The IS relation is standard:

Y = C (Y - T) +1 (r ) + G.

Assume that the price level is fixed in the short run.

1. Solve for the tax multiplier (Hint: you might want to use Cramer’s rule). What is its sign and size?

Solution:

We assume that

        [pic 1] 

Derivate the IS equation with respect to T

        [pic 2] 

Derivate the LM equation with respect to T

        [pic 3] 

Substituting back in the IS equation

        [pic 4] 

1. Contrast your results to the multiplier obtained in the standard IS-LM model with taxes not appearing in money demand. Explain the difference intuitively.

Solution:

        [pic 5] 

        [pic 6] 

In answering this question, you may need some of the following plausible parameter values.

Interest rate elasticity of investment = 0.8

Interest rate elasticity of money demand = 0.1

Income elasticity of money demand = 1.0

Investment-Income Ratio = 0.15

Marginal Propensity to Consume out of Income = 0.5

1. Is the following statement True, False, or Uncertain? Explanation determines grade. The answer should be specific and concise, preferably not exceeding a couple of sentences.

‘A high Marginal Propensity to Save makes the LM curve flat.’

Answer: FALSE

AS MPS grows, the MPC goes down, so the corresponding multiplier will go down as well. The lower value of this multiplier will give us the less increase in equilibrium income and the IS curve will be steeper. But the change in MPC or MPS does not affect the slope of the LM curve directly, so it is the parameter only for MPC.

1. Consider the production function Y = AK + BL, where A and B are positive constants. Assume that population grows at the constant rate of n and that capital depreciates at the constant rate of [pic 7].

1. Is the production function a neoclassical one?

Solution:

Yes. The production function is CRS but does not exhibit everywhere positive and diminishing marginal products or Inada conditions.

Reference: https://en.wikipedia.org/wiki/Inada_conditions

1. Write the production function in intensive form. What is the marginal product of capital per capita? What is the average product of capital per capita?

Solution:

If we write K/L as k and Y/L as y then in intensive form then

        [pic 8] 

        The marginal product of capital per capita is A.

        The average product of capital per capita is A+B/k.

1. Write down the fundamental capital accumulation equation of the Solow model. Derive the equation for the growth rate of capital per capita.

Solution:

The fundamental capital accumulation equation of the Solow model is the following