# If all quantities produced rise by 10 percent, and all prices fall by 10 percent, which of the following occurs?

I am having a hard time deciding for this question:

If all quantities produced rise by 10 percent, and all prices fall by 10 percent, which of the following occurs?

A) Real GDP rises by 10 percent, while nominal GDP falls by 10 percent.

B) Real GDP rises by 10 percent, while nominal GDP is unchanged.

C) Real GDP is unchanged, while nominal GDP rises by 10 percent.

D) Real GDP is unchanged, while nominal GDP falls by 10 percent.

I think it is either A or B, because I know that real GDP rises but i'm not sure what happens to the nominal GDP. if anyone can help, it would be much appreciated.

It helps to write out things as (simple but) proper equations. Denote production as $Y$ and prices as $P$

It is given that

$$Y_{t+1} = 1.1 Y_t \\ P_{t+1} = 0.9 P_t$$

Nominal GDP is given by $P_t Y_t$

$$P_{t+1}Y_{t+1} = 1.1 Y_t \cdot 0.9 P_t \\ = 1.1\cdot 0.9 \cdot Y_t P_t$$

So nominal GDP changed by $1.1 \cdot 0.9 = 0.99$ - it dropped by one percent.

### So which answer is it?

I assumed that the initial value is base value for the description of the relative changes. If, instead, we have that the larger value is base for the relative change,

$$0.9 Y_{t+1} = Y_t \\ P_{t+1} = 0.9 P_t$$

we get that $$P_{t+1}Y_{t+1} = \frac{1}{0.9} Y_t \cdot 0.9 P_t = Y_t P_t$$

• nominal GDP does not change.

All quantities produced rise by 10% and all prices fall by 10%.

Let's say,

Year 1 2013; Q = 10; P = $10; Nominal GDP (10*10) = 100; Real GDP (10*10) = 100; GDP Deflator ([100/100]*100)= 100 Year 2 2014; Q = 11 (10% increase); P =$9 (10% fall); Nominal GDP (11*9) = 99; Real GDP (11*10) = 110; GDP Deflator ([99/110]*100) = 90 (10% decrease from base year 2013)

Year 2 shows a 10% decrease in GDP from year 1. Nominal GDP went from 100 in year 1 to 99 in year 2, indicating a 1% decrease from year 1 to year 2. Real GDP went from 100 in year 1 to 110 in year 2, indicating a 10% increase from year 1 to year 2. Since your question doesn't factor in the 1% decrease in nominal GDP, I would have to say that the answer is B: real GDP rises by 10% and nominal GDP remains unchanged. This is because the decrease in nominal GDP is so small, and closer to 0% than 10%.