Athens University of Economics and Business Department of Economics

M.Sc in Economic Theory International Macroeconomics Prof. George Alogoskoufis

Spring Semester 2015-16

Exercise 1 Financial Openness, the Current Account and Economic Welfare

Consider an economy lasting for two periods, t=1,2. Output Υ is produced according to a production function of the form,

! (1)

where L is total employment and Αt the productivity of labor in period t. In this economy there are N identical households, and each household supplies one unit of labor in every period.

The productivity of labor is higher in period 2 than in period 1, according to,

! (2)

where g>0.

The representative household selects its consumption path so as to maximize the inter-temporal utility function,

! (3)

under the constraint,

! (4)

where ct=Ct/N is consumption per household, yt=Yt/N is income per household, t=1,2, u is a concave periodic utility function, ρ>0 is the pure rate of time preference and r is the real interest rate at which households can borrow and lend between periods 1 and 2.

1. Derive and interpret the first order conditions for the maximization of the utility of the representative household.

2. Analyze diagrammatically the macroeconomic equilibrium of this economy under financial autarky. 3. Analyze diagrammatically the macroeconomic equilibrium of this economy under financial

openness, assuming households can borrow and lend freely from the rest of the world, at an exogenous international real interest rate r*. Analyze and discuss the path of the trade balance and the current account.

Yt = AtL

A2 = (1+ g)A1

U = u(c1)+1

1+ ρu(c2 )

c1 +c21+ r

= y1 +y21+ r

Professor George Alogoskoufis, International Macroeconomics

4. Discuss the differences between a financially autarkic and a financially open economy. 5. Assume that the per period utility function of the representative household takes the form,

! (5)

Calculate the path of output, consumption and the real interest rate in conditions of financial autarky, assuming the following parameter values: Α1=1, g=0.5, N=100, and ρ=0,5.

4. Under the same assumptions as in question 5, calculate the path of output, consumption and the current account, if the economy is financially open, and can borrow and lend freely at a real interest rate r*=0.75.

5. Explain the differences in the inter-temporal utility of the representative household between autarky and openness.

6. Assume now a world economy, consisting of two economies, similar to the economy we have described so far. These two economies are the Home Economy (H) and the Foreign Economy (F). The two economies differ only with respect to the initial productivity of labor A, and the rate of growth of productivity g. For the Home Economy, A1H=1 and gH=0.5, and for the Foreign Economy, A1F=1.1 και gF=0.2. (A). Calculate the path of output, consumption and the real interest for each economy, under financial autarky, assuming logarithmic preferences as in (5), and N=100, ρ=0.5 for each economy. (B). Under the same assumptions, calculate the path of output, consumption and the current account for each economy, as well as the international real interest rate, under financial openness, when the two economies can borrow and lend freely between them.

7. How do you explain the differences in output, consumption and economic welfare in the two economies between financial autarky and financial openness?

u(ct ) = lnct

!2