Let's say that the economy consists of 100 people. Each person is to divide 1 unit of time between work and leisure given the wage rate w (paid on the labor market). Each person also receives dividends of T. The final total profit of this firm is n. The person's utility function depends on consumption c and leisure I and it is assumed to satisfy u(c, l) = 0 ln(c) + (1 - 0) ln(l), where 0 € (0, 1). On the flip side of the market, there are firms who hire workers and produce output. The representative firm operates with a Cobb-Douglas production technology Y = 2K ¹N ², Z = total factory productivity K = fixed amount of capital. Each of these firm's employees receive a wage of w (total labor cost of the firm is equal to wN). The profit is then given back equally to the shareholder as dividend income. G=0 0=3,2=1, K = 1600. Let's say initially 1. Write the equation that will show relation between each person's dividend income and firms total profit П. 2. Write the consumers budge constraint and maximization problem. Plot these 3. Write down the maximization problem of the firm. 4. Write down the government budget constraint. 5. Find the equilibrium price w, allocations c, N