4) Consider a 2-period model that we studied in a class. Household receives e1 units of

consumption goods at period 1 and e2 units of consumption goods at period 2. There are bonds

and each bond gives y unit of consumption goods at the end of period 2. Each household has 1 unit

of bonds in period 1. Bonds are traded at period 1 at the market price p in terms of consumption

goods. Household decides the quantities of consumption "c1", "c2" for each period and the quantity

of bond holding "q" to maximize his/her utility. Thus, the household's problem can be written as

max

c1,c2,q

{log(c1) + log(c2)}

Subject to

c1 + pq p + e1

c2 yq + e2

c1 0

c2 0

0

Here, "log" is natural log. Thus, log(x)=ln(x) more precisely.

4-1) Solve the above maximization problem of household and derive the demand for the asset as a

function of asset price. Describe the condition under which households have positive demand for

the asset, i.e., q>0. Also, describe the condition under which households have no demand for the

asset, i.e., q=0. (40 points)

4-2) Analyze the effects of e, e, y, p on bond's demand q when q>0 and provide intuitive

explanation for the effects of each parameter on bond's demand (20 points)

4-3) Using equilibrium market clearing condition, i.e., demand=supply, derive bond's price p. (10

points)