PLEASE SHOW ALL THE DETAILS!! THX! A consumer has rational expectations, lives f
ID: 1169435 • Letter: P
Question
PLEASE SHOW ALL THE DETAILS!! THX!
A consumer has rational expectations, lives for 3 periods and receives labor income of $200 in each period. She begins period 1 with no wealth and intends to end period 3 with no wealth. She makes her consumption decisions with the intent of keeping consumption constant throughout her lifetime. Assume that price level is constant and that the real interest rate is equal to zero in every period. This consumer is able to save or borrow as much as she wishes, providing she repays any debts she may have incurred by the end of the third period. During her lifetime our consumer receives two pieces of news: In period 1, the government announces a tax of $150 is to be introduced in period 3. In period 2 Canadian courts find Bryan Adams guilty of producing some of the worst music ever heard. He is forced to make a one time payment of $100 to every Canadian as compensation. How much does she consume in the first period? What is her wealth at the end of that period? Carefully explain your answer. How much does she consume in the second period? What is her wealth at the end of that period? Carefully explain your answer. How much does she consume in the third period?Explanation / Answer
Income = Consumption + Savings
Total income in 3 periods = $200 x 3 = $600
Since she intends to end up with no wealth, her total income = total consumption during 3 periods.
So, she intends to consume $600 in 3 periods.
(a) Period 0:
Income = $200
Tax to be paid in period 3 = $150.
Available for consumption (all 3 periods) = $600 - $150 = $450
Therefore, she will consume $450 / 3 = $150 in period 1 (Since she intends to keep consumption unchanged every period).
Wealth at end of period 1 = $200 - $150 = $50
(b) Period 2: Income $200
There is announcement of addition $100 as income.
So, total income in periods (2 + 3) = $200 + $200 + $100 = $500
Total wealth = $500 + $50 (Period 1 savings) = $550
She will consume $550 / 2 = $275 in period 2.
Wealth at end of period 2 = $200 + $50 - $275 = $25
(c) Period 3: Income $200
Beginning wealth = $25
Add to it: Income for the period $200.
Total wealth = $225
Out of this amount, $150 to be paid for taxes.
Remaining wealth = $225 - $150 = $75
So she will consume $75 to make sure she ends up with zero wealth.
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