Instead of Calvo (1983), we follow Rotemberg (1982) to incorporate nominal stickiness. In the model, monopolistic...

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Instead of Calvo (1983), we follow Rotemberg (1982) to incorporate nominal stickiness. In the model, monopolistic firm jpays (P-1) P, to change its price. In other words, the firm can reset its price at every period, but this action is costly. There are an infinite number of firms, indexed by je [0, 1]. The firm j in period t optimizes the price Pt+k(i) to maximize the following present-valued profits: Pt+ k(j) ΣX=0 - 1) ² Pirk], *Pour [P₁+k(1)Ye+k (j) — W₁+kYe+k (1) – ž (P4-10) B63 P4 P where demand for its goods is given by Yi(j) = (PL)) Pt is the aggregate price; Y, is aggregate output; W, is a nominal wage; and 0< 3 < 1 is a discount factor. 1. Solve the first-order condition with respect to Pt(j). Y₁. 0= (1 € + eur) Y - ITt (1+₁) +BYEtt+1(1+T+1). P Here, use the definitions of wt=W and πt = Pt-1 (5) 2. In this model, equilibrium is symmetric. That is, all firms set the same price, so we have Pt(j) = Pt for all j. Using this symmetry, show that we can simplify the above first-order condition to derive the following equation: 1. (6) (7) 3. Find the steady state conditions. We assume that the growth rate of the real economy is zero and the inflation rate is also zero in the steady state. 4. Log-linearize the equation around the steady state and derive the New Keynesian Phillips curve. Instead of Calvo (1983), we follow Rotemberg (1982) to incorporate nominal stickiness. In the model, monopolistic firm jpays (P-1) P, to change its price. In other words, the firm can reset its price at every period, but this action is costly. There are an infinite number of firms, indexed by je [0, 1]. The firm j in period t optimizes the price Pt+k(i) to maximize the following present-valued profits: Pt+ k(j) ΣX=0 - 1) ² Pirk], *Pour [P₁+k(1)Ye+k (j) — W₁+kYe+k (1) – ž (P4-10) B63 P4 P where demand for its goods is given by Yi(j) = (PL)) Pt is the aggregate price; Y, is aggregate output; W, is a nominal wage; and 0< 3 < 1 is a discount factor. 1. Solve the first-order condition with respect to Pt(j). Y₁. 0= (1 € + eur) Y - ITt (1+₁) +BYEtt+1(1+T+1). P Here, use the definitions of wt=W and πt = Pt-1 (5) 2. In this model, equilibrium is symmetric. That is, all firms set the same price, so we have Pt(j) = Pt for all j. Using this symmetry, show that we can simplify the above first-order condition to derive the following equation: 1. (6) (7) 3. Find the steady state conditions. We assume that the growth rate of the real economy is zero and the inflation rate is also zero in the steady state. 4. Log-linearize the equation around the steady state and derive the New Keynesian Phillips curve.

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To solve the given model and derive the New Keynesian Phillips curve lets go through the steps 1 Sol... View the full answer