## Single Equation Models and Multiple Equation Models

Although sometimes the problem we are trying to analyze may be captured in a single-equation model, there are many instances where two or more equations are necessary. Interactions among a number of economic agents or among different sectors of the economy typically cannot be captured in a single equation, and a system of equations must be specified and solved simultaneously. We can extend our earlier example to illustrate this.

Consider first the demand and supply of two goods. We denote the demands by q" and q[\ and the supplies by qf and q*, where the subscripts I and 2 identify which good we are referring to. Now, as before, we may specify how demands and supplies are related to the prices of the two goods, but this time recognizing that the demand for and supply of good 1 may depend on both its own price and on the price of good 2. Recognition of this fact gives rise to an interdependence between the two markets. For simplicity, suppose that the demand for each good depends on both prices, while the supply of each good depends only on the good's own price. The question we are asking is: If the interdependence between two goods takes this form, what arc the consequences for the equilibrium price and quantity traded in each market in equilibrium? Again, as before, we will restrict ourselves to linear relationships only. We may write

</," = a -feipi 4- fapz. bf,.bz> 0 (1.3)

Notice that in addition to incorporating the usual negative relationship between the demand for a good and its own price, we have included a specific assumption about the cmss-price effects, namely thai these goods are substitutes. 11"ihe price of oood I increases, the demand for good 2 increases, and vicp vervĀ« Spuing cupply equal to an exogenous amount iit each market gives us ci + b-> pi - g*

Pi and solving gives

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