Assume an economy with 1,000 consumers. Each consumer has income in the cur-

rent period of $50 and future income of $60, and pays a lump-sum tax of $10 in the

current period and $20 in the future period. The market real interest rate is 8%. Of the 1,000 consumers, 500 choose optimally to consume $60 in the future, while 500 consume $20 in the future. This suggests that we have two groups of consumers: Group 1 and Group 2, each with a total number equal to 500. Government can finance its spending in the current period using either debt or taxes.

1. Using consumer budget constraints in the current and future period, determine the value of current consumption and saving of each type of consumer (let c1 and s1 denote the consumption and saving of a consumer in Group 1. c2 and s2 denote the consumption and saving of a consumer in Group 2)

Determine the value of: a. The aggregate private saving Sp (of the 1,000 consumers) b. The aggregate current consumption C and future consumption C (of the 1,000 consumers) c. The current-period government deficit (G T ) d. The quantity of debt B issued by the government in the current period