# Macroeconomics Homework Assistance

February 14, 2020 No Comments
Macroeconomics Assignment

1. Consider a two period neoclassical consumption model where an individual has the following utility function:

U(C1,C2)=ln(C1)+ßln(C2)

Where C1 is consumption in the current period, C2 is the consumption in the future period and ß is the discount factor on future consumption.
Suppose the real interest rate is 10%, the individual has a current income of £5000 and a future income of £22000. The individual pays no tax.

What is the individual’s inter-temporal budget constraint? Explain (4 marks).
The general form of the Euler equation is u’(C1) = ßu’(C2) What is the individual’s specific Euler equation? Explain (4 marks).
Using the inter-temporal budget constraint and Euler equation from i) and ii) solve for current consumption (C1) and future consumption (C2)(4 marks).
Is the individual a borrower or saver? Explain (3 marks).
Assume interest rates rise to 15%. Would current consumption rise or fall? Would future consumption rise or fall? Explain (Hint: you don’t need to calculate this) (5 marks).

2. Consider the following production function:

Y=K0.4N0.6

Assume the rate of population growth is 5% (n = 0.05) and the saving rate is 15% (s = 0.15). Solve for the long-run steady-state capital-labour ratio, labour productivity and consumption per worker. (5 marks)
Assume the saving rate has been raised to 40% (s = 0.4) as a result of a fiscal surplus. Calculate the new steady-state capital-labour ratio, labour productivity and consumption per worker. Was the fiscal policy a success? (5 marks)
Assume the saving rate has been raised to 45% (s = 0.45) as the result of a fiscal surplus. Repeat the calculations from part ii) with this higher savings rate. Evaluate this policy and indicate the Golden Rule savings rate. (5 marks)
Now assume the production function is given by: