International Macroeconomics EC201
International Macroeconomics
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International Macroeconomics
EC201
From “International Macroeconomics” by Schmitt-Grohé, Uribe, Woodford
Motivation
• In the previous chapter we have considered an endowment economy
• Now we introduce production.
• Factors affecting firms’ investments will also affect households’ saving decisions
International Macroeconomics, Chapter 4
• The economy is populated by a large number of households and firms
• It lasts for two periods, 1 and 2. In period 1 firms invest in physical capital, which
they used to produce goods in period 2
• Production Function: !" = $"%('()
• $">0 is an efficiency parameter
• % . is an increasing and concave function
• '( is investment in capital in period 1
• Assumptions: , % 0 = 0, ,, %′ . >0, ,,, %′′ . <0
• MPK = $"%′('()
International Macroeconomics, Chapter 4
Investment Decision of Firms
International Macroeconomics, Chapter 4
The production function
International Macroeconomics, Chapter 4
Increase in Efficiency
• Firms borrow in period 1 to finance purchases of investment goods.
• Amount of Debt: 0(1= '(
• Firms borrow at the interest rate 2(
• They repay the loan in period 2, including interest: (1 + 2()0(1
• Firms profit in period 2:
• 5"= $"%('()-(1 + 2()0(1
• 5"= $"%('()-(1 + 2()'(
• Optimal Investment: $"%6 '( = (1 + 2()
International Macroeconomics, Chapter 4
Investment Decision of Firms
International Macroeconomics, Chapter 4
Optimal Investment
International Macroeconomics, Chapter 4
Interest Rate Increase and Efficiency Increase
International Macroeconomics, Chapter 4
Investment schedule
• '( = '(2(, $")
• 5(= $(%('7)-(1 + 27)071
• 071= '7
• The economy starts in period 1. All the variables at time 0 are pre-determined
• Efficiency in period 1 is exogenous
• Firms cannot affect profit in period 1
International Macroeconomics, Chapter 4
Investment Decision of Firms – period 1
• Households own firms
• 879 : period-0 endowment of units of bond
• Budget Constraint in period-1::( + 8(9 − 879 = 5( + 27879
• Budget Constraint in period-2::" + 8"9 − 8(9 = 5" + 2(8(9
• Optimum: 8"9<0
• Transversality condition: 8"9 ≥0
• Hence: 8"9 =0
International Macroeconomics, Chapter 4
Households
• Budget Constraint in period 2 :" = Π" + 1+ 2( 8(9
• Eliminating 8(9 from the two constraints, they collapse into:
:( + :"1 + 2( = Π( + Π"1 + 2(+(1 + 27)879
• Optimality condition (as for the endowment economy)>?(@?,@A)>A(@?,@A) = 1 + 2(
International Macroeconomics, Chapter 4
Households
• Small open economy: 2( = 2∗
• Initial net international investment position:87∗ = 879-071
• Economy’s intertemporal resource constraint:
:( + :"1 + 2(+ '( = $(%('7)+ $"%('()1 + 2( +(1 + 27)87∗
International Macroeconomics, Chapter 4
Equilibrium – step 1
• An equilibrium in the production economy is an allocation {:(, :",'(,2(} satysfing:2( = 2∗$"%6 '( = (1 + 2()
>?(@?,@A)>A(@?,@A) = 1 + 2(
:( + :"1 + 2(+ '( = $(%('7)+ $"%('()1 + 2( +(1 + 27)87∗
Given the initial capital stock, '7 , initial foreign asset position including
interest,(1 + 27)87∗ , the world interest rate, 2∗ , and the level of productivities in
periods 1 and 2, $( and $"
International Macroeconomics, Chapter 4
Equilibrium – Definition
• Output in period 1 (pre-determined): !( = $(% '7
• Trade balance in period 1: C8(= !(-:(-'(
• Current Account in period 1: :$(= C8( + 2787∗
• Output in period 2: !" = $"% '(
• Trade balance in period 2: C8"= !"-:"
• End of Period 1 net investment position: 8(∗ = :$(+87∗
• Current Account in period 2: :$"= C8" + 2(8(∗
• National Savings: D(= !(+2787∗-:(
International Macroeconomics, Chapter 4
Trade Balance and Current Account
• National Savings: D(= !(+2787∗-:(
• Consumption only endogenous variable
• From Households’ problem we know that Consumption is a function of the
exogenous interest rate
• Effect of an increase interest rate:
1. Substitution effect: higher 2(, lower :(
2. Income effect: if household is a borrower (879<0), higher 2(, lower :(. if household
is a saver(879>0), higher 2(, higher :(
ASSUMPTION on Preference: SE dominates IE
3. Income effect from profit: higher 2(, lower period-2 profits, 5".