# Macroeconomics Homework Assistance

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)