ECON2102
Assignment 3:
Consumption, Fiscal Policy and International Trade
Term 1 - 2025
• Please include a complete and signed cover sheet (available on Moodle).
• We will mark Part A, section a) and Part B, section a) and c).
• You are free to type or handwrite your solutions. If you prefer to type them, make sure to use Microsoft Word equations (or equivalent) to write down your equations properly, otherwise reserve a space to handwrite them. If you prefer to handwrite the whole assignment or parts of it, make sure the handwriting is clear, well-organised and legible.
• Please read the questions carefully and go straight to the point.
• Please submit a single pdf file (including the assignment cover sheet).
Part A: Consumption
Suppose that a household lives for two periods and has a utility function and intertemporal budget constraint as follows:
a) Derive step by step the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation.
b) Find a solution for optimal consumption in both period 1 and 2 as a function of the parameter β as well as the variables r, y1 and y2.
c) What is the ceteris paribus effect on consumption today (c1) and tomorrow (c2) of the following shocks:
(i) An increase in β .
(ii) A decrease in lifetime income.
(iii) An increase in Y.
d) Is there a condition where c1= c2 ? If so, what value must β assume?
Part B: Fiscal Policy
Consider an economy existing for four periods following the government budget constraint as follows:
Bt+1 = (1 + i)Bt + Gt — Tt
a) Define each of the variables above and explain, in words, why the equality holds. Re-write this budget constraint during each of the four periods that the economy exists (for t=1, t=2, t=3 and t=4).
b) The Australian government is trying to decrease the country’s stock of debt. Using the equation above, discuss two possible ways this could be achieved using fiscal policy, only. What challenges do you anticipate? (Hint: think of how tax collections change given changes to government spending).
c) Using the elements in the equation above, discuss the likely effects on the future stock of debt (Bt+1) of an expansionary monetary policy. Explain.
d) What will the equation look like in the fourth period and what does this imply for the economy as a whole?
e) Using backwards iteration from the fourth period, form. and interpret (in at least two sentences) the intertemporal government budget constraint for this economy.
Part C: International Trade
Suppose there are two goods, steel and wheat. The world consists of four economies: Gryffindor, Hufflepuff, Ravenclaw and Slytherin. The only production input is labour and one unit of labour can produce steel and wheat in these countries according to the following table:
|
Country
|
Tonnes of steel
|
Tonnes of wheat
|
|
Gryffindor (G)
|
5
|
5
|
|
Hufflepuff (H)
|
5
|
10
|
|
Ravenclaw (R)
|
10
|
5
|
|
Slytherin (S)
|
10
|
10
|
a) Prices are expressed in units of tonnes ofwheat so the price of a tonne of wheat is 1. What is the prices ofa tonne of steel in each economy when there is no trade?
b) Now suppose we let two countries trade with each other (while the others are closed). There are six possible trading partners: GH, HR, RS, GR, HS, GS. For each case explain who exports which product and why?