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Answer to Question #66254 in Macroeconomics for boset

Question #66254
max E0( ln(c0) + .8 ln (c1) )
subject to
c0+p0s1=p0s0=d0s0
c1=p1s1+d1s1
in which st is the number of trees owned in period t. Suppose that s0=1 for each individiual and d0=2. In addition , assume that d1=1 with probability 1/4, that d1=2 with probability 1/4, and that d1=4 with probability 1/2 so that E0(d1)=2.75. Note that, in equilibrium ,i) trees are worthless in period 1 (i.e. p1=0) and ii) s0=s1=1 for all individuals.
a) use a cost /benefit analysis to show that p0=0.8*do in equilibrium .
b) from the expression for p0 in question a) , one can conclude that p0 increases whenever d0 increases. Explain the economic rationale behind this fact.
c) show that the price of a discount bond which pays 2 fruits with certainty in period 1 is 1.6.
d) Calculate the expected net rate of return i) on a tree,ii) on the bond discussed in c) Explain how the rate of return on bond differs from that on trees.
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