The coronavirus pandemic has profoundly affected the World economy for the past year. Several countries already have their COVID vaccine rollout well under way and, for most nations, the number of new COVID cases has been falling since March. India, nonetheless, is currently facing an new coronavirus outbreak, with a record number of new cases despite the country's vaccination effort. In this question, we consider the repercussions of the COVID crisis in India in 2021. Interpret the impact of these changes as a negative shock to India's output.

a. (10 points) Suppose the Indian government decides to implement a new lockdown in the country and, as a result, annual production in the India drops to Q0 = 50 in 2021. Assume that next year, the economy recovers and annual output is now Qt = 100, t 1. If the real annual interest rate is 10%, write down the present value of consumption (PVC) starting in 2021. Assume the initial wealth is zero and the long run budget constraint (LRBC) holds.

b. (10 points) Consider the same output path as in a, but suppose now India is able to fully access international financial markets. Propose a Trade Balance sequence (ie, a debt and repayment plan) that would allow the Indian economy to smooth consumption while satisfying its LRBC.

c. (10 points) Several doctors and health experts have been pressuring president Biden's administration to donate coronavirus vaccines to India, but there is still some uncertainty about whether the U.S. will ship vaccine doses to India by the end of this year. Consider 2 states of the world: V, where the US ships vaccine doses to India and NV, where no vaccine dose is shipped. Suppose there are only two countries in this world: the US and India, and the extra vaccine shots are produced exclusively by American companies. Both countries desire to smooth consumption, and all income takes the form of capital income. Suppose state V happens with 50% probability and increases the output of India from 50 to 100, and the output of the US decreases from 200 to 180, while state NV reduces India's output from 50 to 45, leaving the US unaffected at the output level of 200. Devise a table with two rows corresponding to each state (rows marked V and NV) and in three columns show income to three portfolios: 100% of the India's capital (IND), 100% of US capital (US) and the portfolio of 50% IND + 50% US. Will diversification of capital eliminate consumption risk in the portfolio of 50% IND + 50% US? Explain, making sure you discuss in your answer how this donation could impact the US and India's economies .