问题


There is a single choice question about high school macroeconomics. Answer the question by replying A, B, C or D.
Question: If the consumer price index (CPI) increases by 2 percent and your nominal income increases by 8 percent your real income has approximately
A. increased by 4 percent.
B. decreased by 4 percent.
C. increased by 6 percent.
D. decreased by 6 percent.
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

C		 C
deepseekr1

The question involves calculating the change in real income given a 2% increase in the Consumer Price Index (CPI) and an 8% increase in nominal income. Real income adjusts nominal income for inflation. The approximate formula for the percentage change in real income is:

\[
\text{Real Income Change} \approx \text{Nominal Income Change} - \text{Inflation Rate (CPI Increase)}
\]

Applying this:
\[
8\% \, (\text{nominal}) - 2\% \, (\text{inflation}) = 6\% \, \text{increase in real income}.
\]

To verify, if nominal income rises from $100 to $108 (8% increase) and prices rise by 2%, the new price level is 1.02. Real income becomes:
\[
\frac{108}{1.02} \approx 105.88,
\]
which is a **5.88% increase** (approximately 6%). Thus, real income increases by **6%**.

**Answer: C**		 C
gpto1 C C
GPT-4o C. increased by 6 percent. C
llama3.1-70B-Instruct

C		 C
llama3.1-405B-Instruct

C		 C
DeepSeek-Coder-V2 C C
Qwen2-72B-Instruct C. increased by 6 percent. C
baichuan4 C. increased by 6 percent. C
doubao C. increased by 6 percent.

Real income = Nominal income / (1 + inflation rate). Here, inflation rate is given as 2% (increase in CPI), and nominal income increases by 8%. So real income has increased by approximately 6% (8% - 2%).		 C
minimax C. increased by 6 percent.

Explanation: Real income is calculated by adjusting nominal income for inflation. If the CPI increases by 2 percent, that means prices have increased by 2 percent. If your nominal income increases by 8 percent, but prices have increased by 2 percent, your real income has increased by the difference between the two percentages, which is 8% - 2% = 6%.		 C
kimi A. increased by 4 percent.

Explanation: Real income is calculated by adjusting nominal income for inflation. If the CPI increases by 2 percent, it means that the cost of goods has increased by 2 percent. If your nominal income increases by 8 percent, you are earning more money, but the purchasing power of that money has decreased due to inflation.

To calculate the real income increase, you can use the following formula:

Real Income Increase = (Nominal Income Increase) - (CPI Increase)

Real Income Increase = (8%) - (2%) = 6%

So, your real income has increased by 6 percent. However, since the options provided do not include 6 percent, and the closest option is A, which suggests an increase of 4 percent, it seems there might be a mistake in the options given. If we assume that the increase in real income is less than the nominal income increase due to inflation, then the closest correct answer would be A, but it should be noted that the actual increase is 6 percent.		 C
wenxinyiyan C. increased by 6 percent.

Explanation:

Real income is a measure of income that takes into account the effect of inflation or deflation on purchasing power. It is calculated by dividing nominal income by the consumer price index (CPI) and then multiplying by 100 to express it as a percentage of base-year income.

In this question, we are interested in the percentage change in real income, which can be approximated by subtracting the percentage change in the CPI from the percentage change in nominal income.

Percentage change in real income ≈ Percentage change in nominal income - Percentage change in CPI

Given that the CPI has increased by 2 percent and nominal income has increased by 8 percent, we can calculate the approximate percentage change in real income as follows:

Percentage change in real income ≈ 8% - 2% = 6%

Therefore, your real income has approximately increased by 6 percent.		 C
zhipu C. increased by 6 percent.

Real income can be approximated by adjusting nominal income for the change in the Consumer Price Index (CPI). The formula for calculating the approximate change in real income is:

\[ \text{Change in real income} \approx \text{Change in nominal income} - \text{Change in CPI} \]

In this case:

\[ \text{Change in real income} \approx 8\% - 2\% = 6\% \]

Therefore, your real income has approximately increased by 6 percent.		 C
gpto1 C C