## Core Concept: Normalizing Prices and Quantities (10 minute read)

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##### Learning Outcome:
After completing this lesson, you will know why prices and quantities are normalized in a model, why normalizing does not affect model results, and how to calculate a normalized price and quantity.

Key points about normalized prices and quantities
Reduces the information needed to produce a CGE model database
Does not affect CGE model results

##### What are Normalized Prices and Quantities?

As you explore the CGE model and its initial equilibrium, you will notice that most prices have a value of "one."  Why are these initial prices set to one?

Recall that the SAM reports the values of all transactions in an economy at a point in time.  The SAM reports only value data, but not prices or quantities. Yet, the results of a CGE model experiment report changes in prices and quantities from their base values. How is this possible?

"Normalizing" prices and quantities allows price and quantity data to be generated from value data alone.  This significantly reduces the information needed to develop a CGE model database. Normalizing sets the price of a good equal to one in the model's currency, such as $1, and interprets the quantity as units per dollar. For example, suppose that the SAM reports that consumers spend$50 on services.  If we set the consumer price of services equal to $1, then we can describe the quantity as 50 units of services. The total value of the purchase remains the same, because (price * quantity) = 50 *$1 = $50. ##### Normalizing Does Not Affect Experiment Results After an experiment, the percent changes in normalized prices and quantities are no different than they would be if we had started with actual price and quantity data. The percent change in value, also, is no different when we normalize prices. Consider this example in which we have actual price and quantity data for the consumer's expenditure on services (table 1). They initially buy 5 units of services for$10 each, with a total expenditure of $50. The model experiment causes the price to fall 20%, to$8, and the quantity demanded to increase 100%, to 10 units.  Expenditure therefore rises 60% to $80. When data are normalized, the same 20% decline in price, to 80 cents, and doubling of quantity to 100 units, results in the same level of consumer expenditure of$80 (\$0.80 * 100).

Table 1.  Experiment results with normalized prices and quantities

Larger version of table available HERE.

Generally, all prices in a CGE model are normalized, but they do not all have an initial value of 1.  Some price are calculated as after-tax values. In the UNI-CGE model, for example, the domestic price of an import of commodity c, pm(c), includes the tariff. Variable pm is initially defined as 1. The world price of that import (pwm(c) - its price when it arrives at the home country's port) is defined as pm minus the tariff on that commodity.  If the tariff is .10 then the initial world price of the import is 0.9.

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