What would be the long-run economic impacts of the COVID-19? Discuss your thoughts based on the Solow growth model.

Question 1

Suppose that every consumer is born without any financial wealth and lives for three periods: young, middle age and old. Consumers work in the first two periods and retire in the last one. Their labour income, which we assume they receive at the end of each period, is $18,000 in the first period, $100,000 in the second and $0 in the last period. Inflation and expected inflation are zero and the real interest rate is 3% per period.

a. What is each person's present discounted value (PDV) of future labour income at the beginning of life (2dp)?

b. Suppose the consumer plans the same (permanent)consumption at the end of each of the three periods of life, . Calculate where the PDV at the beginning of life of lifetime consumption equals the PDV of income (as calculated in a) (2dp). Hint: set = ( + + (+) + (+) ) Suppose now that restrictions on borrowing prevent young consumers from borrowing. The borrowing restriction means that consumers cannot consume more than they earn or have saved from previous periods (cash on hand). If at any time, desired consumption exceeds cash on hand, then consumers are constrained to consume exactly their cash on hand.

C. Derive consumption in each period of life. Explain the difference between your answers here and your answer to (b). (2dp)