According to BEA, in the U.S., real personal consumption expenditure (PCE) was \(\$ 10,811.4\) billion and nominal PCE was \(\$ 11,653.3\) billion in the fourth quarter of \(2013 .\) The PCE deflator was 108.9 and real \(\mathrm{PCE}\) was \(\$ 11,119.6\) billion in the fourth quarter of 2014 Calculate the PCE deflator in 2013 and the percentage change in real \(P C E\) and nominal PCE.

The PCE deflator is a crucial concept in understanding inflation in personal consumption. It measures the changes in the price level of all final goods and services consumed by individuals.

A higher PCE deflator indicates that the general price level has increased, which often means inflation. Conversely, a lower PCE deflator signals a decrease in the general price level, often associated with deflation.

To calculate the PCE deflator, we use the formula: \[ \text{PCE deflator} = \frac{\text{Nominal PCE}}{\text{Real PCE}} \times 100 \] Here, nominal PCE is the current dollar value of goods and services, while real PCE is the dollar value adjusted for inflation. This ratio helps us understand the impact of changing prices on total expenditure. For the year 2013, with nominal PCE at \$11,653.3 \ billion and real PCE at \$10,811.4 \ billion, the PCE deflator is: \[ \text{PCE deflator}_{2013} = \frac{11,653.3}{10,811.4} \times 100 \approx 107.8 \] This indicates a slight inflation in 2013 because the price level increased by about 7.8% compared to the base year.

Real Personal Consumption Expenditure (PCE) measures the dollar value of goods and services purchased by households, adjusted for inflation. It is a more accurate reflection of the purchasing power of consumers, as it eliminates the effect of price changes over time.

To understand real PCE, think of it as taking the nominal PCE value and removing the inflation component to see the true change in consumption. For example, if we have a real PCE of \$10,811.4 \ billion in 2013 and \$11,119.6 \ billion in 2014, this shows an actual increase in consumption volumes from one year to the next.

The percentage change in real PCE helps capture this growth accurately: \[ \text{Percentage change in Real PCE} = \frac{11,119.6 - 10,811.4}{10,811.4} \times 100 \approx 2.85\text{\text{\text{\text{\text{\text{\textindle}}}}}} \] An increase of 2.85% shows consumers were able to purchase more in 2014, adjusting for inflation.

Nominal Personal Consumption Expenditure (PCE) reflects the total current dollar value of goods and services consumed by households within a period, unadjusted for inflation. It gives an immediate snapshot of consumer spending but doesn't account for price changes over time.

For example, the nominal PCE in 2013 was \$11,653.3 \ billion, representing the total expenditure at the prices prevailing at that time. However, this does not adjust for inflation, meaning it includes the effect of changing prices.

Comparing nominal PCE across periods can be misleading if inflation is not considered, as it may suggest increased spending when in reality, price levels might have risen. For instance, if nominal PCE remains constant, it can indicate no actual increase in consumption. In the exercise, the percentage change in nominal PCE from 2013 to 2014 is zero: \[ \text{Percentage change in Nominal PCE} = \frac{11,653.3 - 11,653.3}{11,653.3} \times 100 \ = 0\text{\text{\text{\text{\text{\text{\textindle}}}}}} \] indicating no change in total expenditure values without inflation adjustment.

Understanding how to calculate the percentage change is critical for analyzing changes over time in economic indicators like PCE.

The formula to calculate percentage change is straightforward: \[ \text{Percentage change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \] This formula shows how much one value has increased or decreased in percentage terms from another value.

Let's apply it to real PCE: given that the real PCE increased from \$10,811.4 \ billion in 2013 to \$11,119.6 \ billion in 2014, we calculate it as: \[ \text{Percentage change in Real PCE} = \frac{11,119.6 - 10,811.4}{10,811.4} \times 100 \approx 2.85\text{\text{\text{\text{\text{\text{\textindle}}}}}} \] This shows a 2.85% growth in real purchases by households, indicating healthier economic activity.

Similarly, for nominal PCE which hasn't changed: \[ \text{Percentage change in Nominal PCE} = \frac{11,653.3 - 11,653.3}{11,653.3} \times 100 \ = 0\text{\text{\text{\text{\text{\text{\textindle}}}}}} \] showing no change in consumption nominally. This emphasizes the importance of considering both real and nominal values for a clear economic insight.