Consider an exchange economy with two investors, A and B, and one physical good. Investor, i, lives for two periods, and has lifetime utility given by U(cc)=log(c)+ Blog(c) B=(0,1) i={A,B} where c, is consumption of the good of investor i in period t = {0, 1}. Their endowments are given by y¹ = {y} y² = {yo,y} where the first component in the endowment vector denotes the investor's endowment of the physical good in period 0, and the second component denotes the investor's endowment of the good in period 1. Importantly, the physical good is non-storable. Each investor may be willing to trade some of period 0 endowment in order to enhance consumption in period 1, or vice versa. Market structure: In period 0, investors can trade in the physical good (or equivalently, trade claims to the physical good), as well as buy and sell "futures" (i.e., promises to deliver one unit of the good in period 1). In period 1, there are no more transactions except that investors execute their promises. Use values for ß = 0.99, y =3, y₁ = 1, y = 2 and y = 3. (a) If q denotes the price of the good in period 0, and q, the price of a “future”, what will be each investor's demand functions for these two goods? Show how you solved for these functions. (b) Normalize the price of the good in period 0 to 1 (i.e., take q = 1), and determine the equilibrium price of a "future", q (c) How many futures does investor A buy?
Consider an exchange economy with two investors, A and B, and one physical good. Investor, i, lives for two periods, and has lifetime utility given by U(cc)=log(c)+ Blog(c) B=(0,1) i={A,B} where c, is consumption of the good of investor i in period t = {0, 1}. Their endowments are given by y¹ = {y} y² = {yo,y} where the first component in the endowment vector denotes the investor's endowment of the physical good in period 0, and the second component denotes the investor's endowment of the good in period 1. Importantly, the physical good is non-storable. Each investor may be willing to trade some of period 0 endowment in order to enhance consumption in period 1, or vice versa. Market structure: In period 0, investors can trade in the physical good (or equivalently, trade claims to the physical good), as well as buy and sell "futures" (i.e., promises to deliver one unit of the good in period 1). In period 1, there are no more transactions except that investors execute their promises. Use values for ß = 0.99, y =3, y₁ = 1, y = 2 and y = 3. (a) If q denotes the price of the good in period 0, and q, the price of a “future”, what will be each investor's demand functions for these two goods? Show how you solved for these functions. (b) Normalize the price of the good in period 0 to 1 (i.e., take q = 1), and determine the equilibrium price of a "future", q (c) How many futures does investor A buy?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider an exchange economy with two investors, A and B, and one physical good.
Investor, i, lives for two periods, and has lifetime utility given by
U(c,c) = log(c)+ Blog(c{) Be(0,1) i={4, B}
where c is consumption of the good of investor i in period t= {0, 1}. Their endowments are
given by
y ={y°•y?}
where the first component in the endowment vector denotes the investor's endowment of the
physical good in period 0, and the second component denotes the investor's endowment of
the good in period 1. Importantly, the physical good is non-storable. Each investor may be
willing to trade some of period 0 endowment in order to enhance consumption in period 1, or
vice versa.
Market structure: In period 0, investors can trade in the physical good (or equivalently, trade
claims to the physical good), as well as buy and sell “futures" (i.e., promises to deliver one
unit of the good in period 1). In period 1, there are no more transactions except that investors
execute their promises.
Use values for ß = 0.99, y =3, y' =1, y" =2 and y" =3.
(a) If q, denotes the price of the good in period 0, and q, the price of a “future", what will be
each investor's demand functions for these two goods? Show how you solved for these
functions.
(b) Normalize the price of the good in period 0 to 1 (i.e., take q =1), and determine the
equilibrium price of a “future", q' .
(c) How many futures does investor A buy?
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