Suppose that an investor with $2 in capital has a logarithmic utility of wealth function: U = ln(ω). The investor has the opportunity to buy into the gamble described in the St. Petersburg paradox. Assume that the investor can borrow without interest and that the gamble payoff is 2ⁱ where i is the number of tosses or outcomes realized before the first head is realized.

a. What is the investor’s current utility of wealth level?

b. How much would the investor be willing to pay for the gamble described in the St. Petersburg paradox?

c. How much would the investor be willing to pay for the gamble described in the St. Petersburg Paradox if his initial wealth level were $1000 rather than $2?

d. What would be your answer to part b if the gamble payoff were to change to 2^2i–1 where i is the number of tosses or outcomes realized before the first head is realized?