Question

Let corn denote per capita consumption of corn in bushels at the county level, let price be the price per bushel of corn, let income denote per capita county income, and let rainf all be inches of rainfall during the last corn-growing season. The following simultaneous equations model imposes the equilibrium condition that supply equals demand:

corn = alpha1 price + beta1 income + mu1
corn = alpha2 price + beta2 rainfall + gamma rainfall2 + mu2
Which is the supply equation, and which is the demand equation? Explain.

Answer 1

`Corn = \alpha_1 *price + \beta_1 * income + \mu_1` --- Demand

`Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2` --- Supply

Explanation:

Given

`Corn = \alpha_1 *price + \beta_1 * income + \mu_1`

`Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2`

Required

Identify the demand and the supply equation.

To identify which is the demand equation and which is the supply equation, we simply look through the constraints of the equation.

For (1):

`Corn = \alpha_1 *price + \beta_1 * income + \mu_1`

We have: Price and Income

For (2):

`Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2`

We have: Price and Rainfall

In (1), price and income determines the demand of a product.

Hence, (1) represents the demand equation

In (2), price and weather condition (rainfall) determines the supply of a product.

Hence, (2) represents the supply equation.