Q3. Financial Accelerator (30 points) Consider a firm j that operates in an infinite horizon, t= 0,1,2,... On its balance sheet at the end of each period t, the firm's asset is composed of capital kjt evaluated at the capital price q, the liability is composed of its debt dit, and the net worth is njt = qtkjt -djt. At the beginning of period t, the firm's asset is evaluated as qkj-1, where kj-1 is the firm's capital that it brought from the previous period t - 1 and q, is the current capital price. The firm's liability is (1+r-1)dj.1-1, which is the sum of the debt dj-1 it borrowed in the previous period 1-1 and the interest r-1d-1 accrued. (revaluation) During period 1, the firm produces output zjif(kj.1,j), where ; is the fixed labor input and zj, is the productivity of firm j, pays wages w,lj, purchases capital by the amount of kjt-kj1-1 at price q, (or sell when kjt - kj-1 < 0), and borrow more by dj (1 + r_1dj,1) (or repay debt when djr - (1 + r_1dj.s1) < 0). (economic activities) The budget constraint for the economic activities of this firm is qr(kjt kj,t1)+wj = Zjtf (kj;,t1,j)+d;jt (1+r1)dj,s1. Each firm j borrows its debt from financial intermediaries. Importantly, the financial intermediaries impose a collateral constraint on the firm such that its total debt dj, cannot be greater than a certain fraction (0 < < 1) of the total value of its physical capital, qkj. In other words, dj