3. (25%) Let us examine a simple model of employment and unemployment. Consider an economy of two production sectors. Denote the sectors by \( i = 1,2 \). Suppose that the economy has a labor force of \( L \), with \( v \) of the labor force being allocated to sector 1 and \( (1 - v) \) of the labor force being allocated to sector 2. Let \( U{i}, E{i}, s{i} \) and \( f{i} \) be the total number of the unemployed workers, the total number of the employed workers, job separating rate and job finding rate in sector \( i \), respectively. A worker is either employed or unemployed. Assume that the labor markets of the two production sectors are completely segregated, and there is no labor mobility across sectors. Answer the following questions.