Question

Suppose an economy produces 5 different goods, \(A, B, C\), \(D\), and \(E\), which have different prices Given data for two different years: $$ \begin{array}{|l|l|l|l|l|} \hline \text { Goods } & \text { quantity } & \text { price } & \text { quantity } & \text { price } \\ \hline \text { A } & 85 & \$ 1.25 & 86 & \$ 1.50 \\ \hline \text { B } & 84 & 0.96 & 50 & 1.30 \\ \hline \text { C } & 225 & 5.60 & 227 & 5.50 \\ \hline \text { D } & 113 & 3.58 & 150 & 3.15 \\ \hline \text { E } & 34 & 2.28 & 66 & 2.35 \\ \hline \end{array} $$ it is necessary to calculate: 1) The value of output in Year 1, in current dollars. 2) The value of output in Year 2, in current dollars. 3) The percentage change in current dollars from Year 1 to Year 2 . 4) The price index for Year 2 to base Year 1 . 5) The real output in Year 2, expressed in Year 1 dollars. 6) The price index for Year 1 to base Year 2 . 7) The real output in Year 1, expressed in Year 2 dollars. 8) The percentage change in real output, in terms of Year 1 dollars, from Year 1 to Year 2 . 9) The percentage change in real output, in terms of Year 2 dollars, from Year 1 to Year 2 . And, give a general evaluation of the economy's performance.

Short answer

In summary, after calculating the value of output, price indices, and real output for both years, we found that the economy experienced changes in output and prices between Year 1 and Year 2. The percentage change in current dollars and real output, in terms of both Year 1 and Year 2 dollars, provide insight into the overall performance of the economy over this time period. Based on these values, the economy may have experienced growth or contraction, as well as changes in inflation. Examining these figures in conjunction with each other helps us understand how the economy has evolved between these two years.

Step-by-step solution

1) Calculate the value of output in Year 1 (in current dollars).

To find the value of output, we will multiply the quantity of each good by its price and add up the values for all goods. For Year 1: Value of output = (Good A quantity * Good A price) + (Good B quantity * Good B price) + (Good C quantity * Good C price) + (Good D quantity * Good D price) + (Good E quantity * Good E price) Using the provided table data, we obtain: Value of output in Year 1 = \((85 * 1.25) + (84 * 0.96) + (225 * 5.60) + (113 * 3.58) + (34 * 2.28)\)

2) Calculate the value of output in Year 2 (in current dollars).

Follow the same steps as in part 1, but this time for the prices and quantities in Year 2. Value of output in Year 2 = \((86 * 1.50) + (50 * 1.30) + (227 * 5.50) + (150 * 3.15) + (66 * 2.35)\)

3) Calculate the percentage change in current dollars from Year 1 to Year 2.

Percentage change in current dollars = \(\frac{Value\;of\;output\;in\;Year\;2 - Value\;of\;output\;in\;Year\;1}{Value\;of\;output\;in\;Year\;1} * 100\)

4) Calculate the price index for Year 2 using Year 1 as the base year.

To calculate the price index, divide the total value of each good in Year 2 by the total value in Year 1, and multiply by 100. Price Index = \(\frac{Total\;value\;in\;Year\;2}{Total\;value\;in\;Year\;1}\) * 100

5) Calculate the real output in Year 2, expressed in Year 1 dollars.

To find the real output, divide the value of output in Year 2 by the price index from part 4, and then multiply by 100. Real Output (Year 2 in Year 1 dollars) = \(\frac{Value\;of\;output\;in\;Year\;2}{Price\;Index} * 100\)

6) Calculate the price index for Year 1 using Year 2 as the base year.

Similarly to part 4, now calculate the price index using Year 2 as the base year. Price Index (Year 2 as base) = \(\frac{Total\;value\;in\;Year\;1}{Total\;value\;in\;Year\;2}\) * 100

7) Calculate the real output in Year 1, expressed in Year 2 dollars.

Use the price index calculated in part 6 to find the real output for Year 1 in Year 2 dollars. Real Output (Year 1 in Year 2 dollars) = \(\frac{Value\;of\;output\;in\;Year\;1}{Price\;Index} * 100\)

8) Calculate the percentage change in real output, in terms of Year 1 dollars, from Year 1 to Year 2.

To find the percentage change in real output, use the real output values from part 5. Percentage change = \(\frac{Real\;Output\;(Year\;2\;in\;Year\;1\;dollars) - Real\;Output\;(Year\;1\;in\;Year\;1\;dollars)}{Real\;Output\;(Year\;1\;in\;Year\;1\;dollars)} * 100\)

9) Calculate the percentage change in real output, in terms of Year 2 dollars, from Year 1 to Year 2.

Similar to part 8, use the real output values from part 7. Percentage change = \(\frac{Real\;Output\;(Year\;2\;in\;Year\;2\;dollars) - Real\;Output\;(Year\;1\;in\;Year\;2\;dollars)}{Real\;Output\;(Year\;1\;in\;Year\;2\;dollars)} * 100\) Based on the results of these calculations, interpret the economy's performance over the two years.

Key concepts

Economic Output Measurement

When we talk about measuring economic output, what we're really looking at is the total value of all goods and services produced by an economy over a specific period of time. This measure, commonly known as Gross Domestic Product (GDP), gives us a snapshot of the economy's size and health.

Measuring GDP can be done in two primary ways: at current prices or at constant prices. When we measure it at current prices, also referred to as nominal GDP, we evaluate the output using the prices that were current for the time period being studied. However, this can sometimes be misleading, as it can be affected by changes in price level due to inflation or deflation.

To address that issue, we can use GDP at constant prices, which adjusts for inflation or deflation. This is also known as real GDP. It separates price changes from quantity changes by using a set of fixed prices from a base year, allowing for a more accurate comparison of economic output over time.

Price Index Calculation

A key tool in economic analysis is a price index, a measure that shows how the average price level of a set of goods and services changes over time. These indices are critical for adjusting payments and comparing economic indicators across different time periods.

To calculate a price index, we select a base year as a standard for comparison, and then we calculate how much the current price of a basket of goods and services has changed in comparison to the base year. The most commonly used price index is the Consumer Price Index (CPI), which measures changes in the price level of a market basket of consumer goods and services purchased by households.

In the given exercise, the calculation of the price index allows us to quantify the effect of price changes on economic output between Year 1 and Year 2, providing the basis for computing real GDP.

Real Output Analysis

Real output analysis allows economists and policymakers to understand the true growth of an economy, unaffected by changes in the price level. By analyzing real output, we can discern whether an increase in GDP is due to actual increased production of goods and services or merely due to higher prices (inflation).

To analyze real output, the value of goods and services produced is adjusted using a price index to reflect prices at a consistent point in time. This deflated measure removes the effects of inflation to show the actual change in volume of production.

In our exercise, after calculating real GDP for Year 1 and Year 2, we can evaluate the economy's performance by comparing these figures. An increase in real GDP would indicate that the economy is genuinely growing, as opposed to an increase in nominal GDP that could just be a result of rising prices.