The figure depicts Matthew's choice of consumption in periods 1 and 2. He has an income of $100 in period 1 and no income in period 2. The interest rate is 20%. Based on the figure... The figure depicts Matthew's choice of consumption in periods 1 and 2. He has an income of $100 in period 1 and no income in period 2. The interest rate is 20%. Based on the figure, which of the following statements is correct?
Understand the Problem
The question is asking about Matthew's consumption choices in two periods based on a given interest rate and his income, and it requires analyzing statements related to the graph provided.
Answer
At A, Matthew makes no savings.
Answer for screen readers
The correct answer is: "At A, Matthew makes no savings."
Steps to Solve
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Identify Income and Consumption Points
Interpret the graph. Matthew has an income of $100 in period 1 and no income in period 2. At point A, he consumes all $100 now, and at point C, he saves all for the future. -
Understanding the Interest Rate Impact
Given the interest rate of 20%, any savings will yield a return when consumed in the second period. Therefore, $100 saved in period 1 will be worth $100 * (1 + 0.2) = $120 in period 2. -
Check Consumption Limits
The feasible consumption limit can be represented:
- Total consumption in period 2 = Total savings from period 1 + interest. At point A, consumption in period 1 is $100 which means no savings. At point C, consumption in period 1 is $0, thus savings are $100, leading to $120 consumption in period 2.
- Verify Each Statement
- Statement 1: If the interest rate increases, the frontier pivots outward. Check if true.
- Statement 2: At point B, we need to find out if $110 is realistic.
- Statement 3: Check the graph at point C for period 1 consumption.
- Statement 4: Confirm if Matthew saves at point A, where all income is consumed.
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Determine Correct Statement
Analyze which of the statements align with the analysis of the graph and the impact of the interest rate on consumption.
The correct answer is: "At A, Matthew makes no savings."
More Information
At point A on the graph, Matthew chooses to consume all of his available income ($100) in period 1, meaning he does not save any for the future. Thus, his consumption in period 1 is maximized at the expense of future consumption.
Tips
- Confusing the meaning of consuming now versus saving for later. Remember, if Matthew consumes all now, his savings in the future will be zero.
- Misinterpreting the graphical depiction of various consumption points and the resulting feasible frontier.
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