13. Consider a world of two countries: Highland (H) and Lowland (L). Each country has an average output of 9 and desires to smooth consumption.

All income takes the form of capital income and is fully consumed each period.

a. Initially, there are two states of the world: Pestilence (P) and Flood (F). Each happens with 50% probability. Pestilence affects Highland and lowers the output there to 8, leaving Lowland unaffected with an output of 10. Flood affects Lowland and lowers the output there to 8, leaving Highland unaffected with an output of 10. Devise a table with two rows corresponding to each state (rows marked P and F). In three columns, show income to three portfolios: the portfolio of 100% H capital, the portfolio of 100% L capital, and the portfolio of 50% H + 50% L capital.

b. Two more states of the world appear: Armageddon (A) and Utopia (U). Each happens with 50% probability but is uncorrelated with the P–F state. Armageddon affects both countries equally and lowers income in each country by a further four units, whatever the P–F state.
Utopia leaves each country unaffected. Devise a table with four rows corresponding to each state (rows marked PA, PU, FA, and FU). In three columns, show income to three portfolios: the portfolio of 100% H capital, the portfolio of 100% L capital, and the portfolio of 50% H + 50% L capital.
Compare your answers to parts

(a) and (b), and consider the optimal portfolio choices. Does diversification eliminate consumption risk in each case? Explain.