The small open economy case We consider a small open economy producing two goods i = 1,2. These goods are produced using only one factor of production, labor. We will denote by a the quantity of labor required for the production of one unit of good i. We will denote by L the labor endowment of the country. The representative consumer in the country has preferences given by the utility function U (C₁, C₂)= a Log C₁+(1-0) Log C₂ We let p, denote the price of good i and w, denote the wage rate in sector i. 1. Derive the relationship determining the competitive supply this econ- omy, given by the vector Q (Q₁, Q2) of produced quantities of both goods, as a function of prices p₁ and p2. Represent graphically the rela- tive supply schedule of good 1. 8, as a function of the relative price Determine the labor market clearing rate w. 2. Represent graphically the set of feasible output combinations (the Pro- duction Possibilities Set) in the (Q₁-Q2) space. How is the competitive relative supply schedule, as a function of the relative price , deter- mined in this graph? 3. Derive the vector of demands C= (C₁, C₂) as a function of goods' prices (P₁-P2). Derive and represent graphically relative demand as a function of the relative price 4. Determine the vector of net demand for each good i, Z₁ = Ci - Q₁, as a function of the relative price . Graphically represent the "offer curve" of the economy (i.e. the locus of combinations of (Z₁, Z₂) reflecting these excess demands). 1
The small open economy case We consider a small open economy producing two goods i = 1,2. These goods are produced using only one factor of production, labor. We will denote by a the quantity of labor required for the production of one unit of good i. We will denote by L the labor endowment of the country. The representative consumer in the country has preferences given by the utility function U (C₁, C₂)= a Log C₁+(1-0) Log C₂ We let p, denote the price of good i and w, denote the wage rate in sector i. 1. Derive the relationship determining the competitive supply this econ- omy, given by the vector Q (Q₁, Q2) of produced quantities of both goods, as a function of prices p₁ and p2. Represent graphically the rela- tive supply schedule of good 1. 8, as a function of the relative price Determine the labor market clearing rate w. 2. Represent graphically the set of feasible output combinations (the Pro- duction Possibilities Set) in the (Q₁-Q2) space. How is the competitive relative supply schedule, as a function of the relative price , deter- mined in this graph? 3. Derive the vector of demands C= (C₁, C₂) as a function of goods' prices (P₁-P2). Derive and represent graphically relative demand as a function of the relative price 4. Determine the vector of net demand for each good i, Z₁ = Ci - Q₁, as a function of the relative price . Graphically represent the "offer curve" of the economy (i.e. the locus of combinations of (Z₁, Z₂) reflecting these excess demands). 1
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:The small open economy case
We consider a small open economy producing two goods i=1,2. These goods
are produced using only one factor of production, labor. We will denote by a
the quantity of labor required for the production of one unit of good i. We will
denote by L the labor endowment of the country. The representative consumer
in the country has preferences given by the utility function
U (C₁, C₂) = a Log C₁ + (1 -a) Log C₂
We let p; denote the price of good i and w, denote the wage rate in sector i.
1. Derive the relationship determining the competitive supply of this econ-
omy, given by the vector Q= (Q1, Q2) of produced quantities of both
goods, as a function of prices p₁ and p2. Represent graphically the rela-
tive supply schedule of good 1, as a function of the relative price
Determine the labor market clearing rate w.
2. Represent graphically the set of feasible output combinations (the Pro-
duction Possibilities Set) in the (Q₁, Q2) space. How is the competitive
relative supply schedule, as a function of the relative price 2, deter-
mined in this graph?
3. Derive the vector of demands C = (C₁, C₂) as a function of goods' prices
(P₁, P2). Derive and represent graphically relative demand as a function
of the relative price.
4. Determine the vector of net demand for each good i, Z; = C₁ - Q₁, as a
function of the relative price Graphically represent the "offer curve"
of the economy (i.e. the locus of combinations of (Z₁, Z₂) reflecting these
excess demands).
1
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