Your Textbook Gives the Following Example of Simultaneous Causality Bias $y _ { 0 }$

Essay

Your textbook gives the following example of simultaneous causality bias of a two equation system:
Y_i = β₀ + β₁X_i + u_i
X_i = $y _ { 0 }$ + $y _ { 1 }$ Y_i + v_i
In microeconomics, you studied the demand and supply of goods in a single market. Let the demand ( $Q _ { i } ^ { D }$ )and supply ( $Q _ { i } ^ { S }$ )for the i-th good be determined as follows, $Q _ { i } ^ { D }$ = β₀ - β₁P_i + u_i, $Q _ { i } ^ { S }$ = $y _ { 0 }$ - $y _ { 1 }$ P_i + v_i,
where P is the price of the good. In addition, you typically assume that the market clears.
Explain how the simultaneous causality bias applies in this situation. The textbook explained a positive correlation between X_i and u_i for $y _ { 1 }$ > 0 through an argument that started from "imagine that u_i is negative." Repeat this exercise here.