The Product Market Equation x = p + q. The Product Market Equation

Comments on the Equations All of the variables in this equation are written using lower case letters Lower case letters are used to indicate that all the variables are rates of change. That is, we are describing “by what percent this value has changed since a year ago.” The definitions of these terms will therefore use phrases such as: “the percent change of …”, “the rate of change of …”, “the growth rate of …”, “the ___ growth rate.”

Spending = Price x Quantity X = PxQ Buying 100 items (Q = 100) at $10 apiece (P = $10) means spending was $1000 (X = $1000) Next year we buy 108 items at $11 apiece means spending was $1188 %Δ Spending = %Δ Price + %Δ Quantity x = p + q* PER CENT CHANGES How to calculate a percent change: %ΔX = (X1 – X0)/X0, which can also be computed as X1/X0 – 1 (Then you multiply by 100% to make it a percent) Q %ΔQ (q) P %ΔP (p) X %ΔX (x) 100 8% 10 10% 1000 18.8% 1 108 11 1188 Notice that is approximately true that %ΔX = %ΔQ + %ΔP That is: 18.8% is about 8% + 10% We are going to pretend that the approximation is exactly correct. It makes things much easier to do so. Throughout the class we will use lower case letters to represent rates of change x = %ΔX, q = %ΔQ, p = %ΔP *the real equation is: x = p + q + pq/100

The Product Market Equation: x = p + q x = the growth rate of total spending (nominal GDP) x = 6% means, “we spent 6% more this year than we did last year.” p = the growth rate of prices (or the “cost of living”) p has an easier name. p is ________ inflation p = 3% means, “on average, the prices of goods are 3% more than last year.” q = real growth (or “the real growth rate”) q = 3% means that we produced 3% more goods and services (“stuff”) than last year.

The Product Market Equation: x = p + q The easiest terms to use for these three concepts are: x = the growth rate of nominal GDP (or “nominal growth.”) p = the inflation rate q = the growth rate of real GDP (or “real growth.”)

The Product Market Equation: x = p + q The equation says that if we spend 6% more this year than we did last year (x = 6), then we are either: we are buying more “stuff.” (real output) and/or paying higher prices for what we are buying, That is, we can think of increases of spending (x) as being split between changes of prices (p) and changes of output (q) It is a good mathematical approximation that the percent changes add up as the equation says they do.

How do we get x, p and q? 1. We can measure spending from things such as tax records. This is the number we actually collect from the economy. We need to collect total spending (X) for two years and then we can compute x as the percent change between the two years. 2. To get inflation, we need to get the PRICE LEVEL (P) for two years and then compute inflation as the percent change between them. The Price Level can be thought of as the cost of a “basket of goods” used by a typical consumer. The inflation rate is therefore the percent increase of a typical basket of goods between two years.

Real Growth. Measuring q To understand “q” (real growth) look at the equation as q = x – p. We have numbers for x and p so we can compute q. Suppose we spend 6% more this year than last year (x = 6). Suppose that prices are, on average, 2% higher than they were last year (p = 2%). The equation says that we must have bought 4% more “stuff” than last year. Of the 6% spending increase, 2% went to higher prices. The other 4% must have gone to real growth (more stuff).

The Product Market Equation: x = p + q This equation draws our attention to something important: the difference between nominal growth (x) and real growth (q) Nominal GDP (X) measures how much we spend, in dollar terms. This is the easiest statistic to collect Real GDP (Q) is often the more significant of the two measures. It is measuring actual production – the economy’s output. Importantly, employment is more closely related to real spending than to nominal spending.

PrM Eq. x = p + q. Some examples #1 6 3 #2 2 8 #3 10 13 #4 -10 -4 What is p (inflation)? 3 10 What is x (nominal growth)? -3 What is q (real growth)? -6 What is q (real growth)? Both year #2 and #3 had x = 10. Which was the better year? Why? Of the three variables – x, p, q – which would you pick to indicate how good the year was? q is the best indicator