Suppose that in 1994 the total output in a single-good economy was

7,000 buckets of chicken. Also suppose that in 1994 each bucket of chicken was

priced at \(10. Finally, assume that in 2015 the price per bucket of chicken was

\)16 and that 22,000 buckets were produced. Determine the GDP price index for

1994, using 2015 as the base year. By what percentage did the price level, as

measured by this index, rise between 1994 and 2015? What were the amounts of

real GDP in 1994 and 2015?

The price in 2015 was $16 per bucket of chicken, and that in 1994 was $10.

The price index for the year 1994:

$$\begin{gathered} PriceIndex=\frac{PriceofCurrentYear}{PriceofBaseYear}\times 100 \\ PriceInde{x}_{1994}=\frac{Pricein1994}{Pricein2015}\times 100 \\ =\frac{10}{16}\times 100 \\ =62.5 \end{gathered}$$

The price index for the base year 2015:

$$\begin{gathered} PriceInde{x}_{2015}=\frac{Pricein2015}{Pricein2015}\times 100 \\ =\frac{16}{16}\times 100 \\ =100 \end{gathered}$$

Percentage change in price level:

$$\begin{gathered} \mathit{I}\mathit{n}\mathit{c}\mathit{r}\mathit{e}\mathit{a}\mathit{s}\mathit{e}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{}\mathit{l}\mathit{e}\mathit{v}\mathit{e}\mathit{l}\mathbf{=}\frac{\mathbf{D}\mathbf{i}\mathbf{f}\mathbf{f}\mathbf{e}\mathbf{r}\mathbf{e}\mathbf{n}\mathbf{c}\mathbf{e}\mathbf{}\mathbf{i}\mathbf{n}\mathbf{}\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{}\mathbf{I}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{x}}{\mathbf{B}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{}\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{}\mathbf{I}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{x}}\mathbf{\times }\mathbf{100} \\ Increaseinpricelevel=\frac{100-62.5}{100}\times 100 \\ =37.5\% \end{gathered}$$

The price per bucket of chicken rose by 37.5% from 1994 to 2015.

Nominal GDP in 2015 is $352,000 ( = $16 × 22,000)

Nominal GDP in 1994 is $70,000 (= $10 × 7,000)

$$\begin{gathered} RealGDP=\frac{NominalGDP}{PriceIndex} \\ RealGD{P}_{2015}=\frac{\$352,000}{100} \\ =\$3,520 \\ RealGD{P}_{1994}=\frac{\$70,000}{62.5} \\ =\$1,120 \end{gathered}$$

Therefore, the real GDP in 2015 was $1,120 and in 1994 (the base year 2015) was $3,520.