Consider a two-period small open economy populated by households and firms with a single good each period. = The preferences of the representative household are described by the utility function u(c₁c₂): (C₁C₂)² where c₁ and c₂ denote consumption in periods 1 and 2, respectively. In period 1, the household receives an endowment of q₁ = 1. In period 2, the household receives profits, denoted by ₂, from the firms it owns. In period 1, the household has access to financial markets where they can borrow or lend at the interest rate r = 10%. The household has a zero asset holding position in period 1. Let the budget constraint in the first period be c₁ + bh =q₁, with b denoting assets purchased in the first period. Firms borrow in period 1 from the international financial market to invest in physical capital and to produce final goods in period 2. Denote by d₁ the amount of debt taken by the firm in period 1. The production technology in period 2 is given by Q₂ = 410.5, where Q₂ and 1₁ denote output in period 2 and investment in period 1, respectively.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Consider a two-period small open economy populated by households and firms with a single
good each period.
The preferences of the representative household are described by the utility function u(c₁c₂) =
(C₁C₂)² where ₁ and ₂ denote consumption in periods 1 and 2, respectively. In period 1, the
household receives an endowment of q₁ = 1. In period 2, the household receives profits,
denoted by T₂, from the firms it owns. In period 1, the household has access to financial
markets where they can borrow or lend at the interest rate r = 10%. The household has a
zero asset holding position in period 1. Let the budget constraint in the first period be c₁ +
b =q₁, with b denoting assets purchased in the first period.
Firms borrow in period 1 from the international financial market to invest in physical capital
and to produce final goods in period 2. Denote by d₁ the amount of debt taken by the firm in
period 1. The production technology in period 2 is given by Q₂ = 410.5, where Q₂ and 1₁
denote output in period 2 and investment in period 1, respectively.
Both firms and households are subject to the same collateral constraint, with ₁ denoting the
value of the collateral. Suppose that ê₁ equals 5. Assume that the economy's initial net foreign
asset position is zero (bg = 0).
Question 1: State the maximization problem of the firm, and compute the firm's optimal levels
of period-1 investment and period-2 profits. Provide intuition.
Transcribed Image Text:Consider a two-period small open economy populated by households and firms with a single good each period. The preferences of the representative household are described by the utility function u(c₁c₂) = (C₁C₂)² where ₁ and ₂ denote consumption in periods 1 and 2, respectively. In period 1, the household receives an endowment of q₁ = 1. In period 2, the household receives profits, denoted by T₂, from the firms it owns. In period 1, the household has access to financial markets where they can borrow or lend at the interest rate r = 10%. The household has a zero asset holding position in period 1. Let the budget constraint in the first period be c₁ + b =q₁, with b denoting assets purchased in the first period. Firms borrow in period 1 from the international financial market to invest in physical capital and to produce final goods in period 2. Denote by d₁ the amount of debt taken by the firm in period 1. The production technology in period 2 is given by Q₂ = 410.5, where Q₂ and 1₁ denote output in period 2 and investment in period 1, respectively. Both firms and households are subject to the same collateral constraint, with ₁ denoting the value of the collateral. Suppose that ê₁ equals 5. Assume that the economy's initial net foreign asset position is zero (bg = 0). Question 1: State the maximization problem of the firm, and compute the firm's optimal levels of period-1 investment and period-2 profits. Provide intuition.
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