Q3. Financial Accelerator (30 points) Consider a firm j that operates in an infinite horizon, t=...

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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 qkj₁-1, 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+r₁-1)dj.1-1, which is the sum of the debt dj-1 it borrowed in the previous period 1-1 and the interest r₁-1d-1 accrued. (revaluation) During period 1, the firm produces output zjif(kj.₁–1,īj), where ī; 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 - kj₁-1 < 0), and borrow more by dj − (1 + r₁_1dj,−1) (or repay debt when djr - (1 + r₁_1dj.s−1) < 0). (economic activities) The budget constraint for the economic activities of this firm is qr(kjt − kj,t−1)+w₁īj = Zjtf (kj;,t−1,Īj)+d;jt −(1+r₁−1)dj,s−1. 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 <p(gikj). 3 (a) Illustrate the evolution of firm j's balance sheet by presenting the balance sheet at three different points in time: at the end of period t-1, at the beginning of period t (reflecting revaluation), and at the end of period 1 (reflecting economic activities). Then, verify that the net worth of firm j at the end of period t, nj, is characterized by njt=nj,₁-1+(9₁-q₁−1)kjs-1-r₁-1dj₁−1+Zji ƒ (kj,s−1, īj) — w₁īj. (b) Show that the the collateral constraint (1) is equivalent to qık ji s -nji- (1) 1-0 (2) (3) Now consider an economy in which there are an infinite number of firms j = [0, 1] that operate as specified above. Moreover, each firm j's productivity, Zjr, is determined by the multiplication of an aggregate productivity A, and idiosyncratic productivity ajt, i.e., Zjt = A₁ajt. (Firms are heterogeneous because of heterogeneous productivity aj, and firm-specific employment size ;) Some firms are constrained (i.e. borrow up to their limit djt = $(qrk jt)), while other firms are not because of the difference in their idiosyncratic productivity ajt. In this economy, consider a small temporary fall of the aggregate productivity A, (i.e., A, falls only in period t). 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 qkj₁-1, 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+r₁-1)dj.1-1, which is the sum of the debt dj-1 it borrowed in the previous period 1-1 and the interest r₁-1d-1 accrued. (revaluation) During period 1, the firm produces output zjif(kj.₁–1,īj), where ī; 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 - kj₁-1 < 0), and borrow more by dj − (1 + r₁_1dj,−1) (or repay debt when djr - (1 + r₁_1dj.s−1) < 0). (economic activities) The budget constraint for the economic activities of this firm is qr(kjt − kj,t−1)+w₁īj = Zjtf (kj;,t−1,Īj)+d;jt −(1+r₁−1)dj,s−1. 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 <p(gikj). 3 (a) Illustrate the evolution of firm j's balance sheet by presenting the balance sheet at three different points in time: at the end of period t-1, at the beginning of period t (reflecting revaluation), and at the end of period 1 (reflecting economic activities). Then, verify that the net worth of firm j at the end of period t, nj, is characterized by njt=nj,₁-1+(9₁-q₁−1)kjs-1-r₁-1dj₁−1+Zji ƒ (kj,s−1, īj) — w₁īj. (b) Show that the the collateral constraint (1) is equivalent to qık ji s -nji- (1) 1-0 (2) (3) Now consider an economy in which there are an infinite number of firms j = [0, 1] that operate as specified above. Moreover, each firm j's productivity, Zjr, is determined by the multiplication of an aggregate productivity A, and idiosyncratic productivity ajt, i.e., Zjt = A₁ajt. (Firms are heterogeneous because of heterogeneous productivity aj, and firm-specific employment size ;) Some firms are constrained (i.e. borrow up to their limit djt = $(qrk jt)), while other firms are not because of the difference in their idiosyncratic productivity ajt. In this economy, consider a small temporary fall of the aggregate productivity A, (i.e., A, falls only in period t).

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Here is my response a Firm js balance sheet End of peri... View the full answer