Macroeconomics

1. Endogenous entry, product variety, and business cycles The baseline model of Ballicie, Glitroni, and Melitz (2012) uader constant-elasticity-of substitution can be written is the following system: pr=c1Ztwr pt=Nt1/(s1) d1=c11C1/Ni vr=wrZtfE Nt=(1)(Nt1+Nt,t1) xR13/=Ciwk x=(1d)Et{Ci+1C1(d1+1+v2+1)} Ct+NC1d1vt=wtLt+Nit logZ1=klogZr1+ct,t,r,1N(0,2) (a) Carefully explain each variable, interpet each cquation, and point out the ingredjents which differ from the real business cycle model. (b) What are the state variables (endogenotes and exogenons)? What are the control variables? (c) What is the quantity of labor employed in product developtuent LtE?. Describe the tradooff in the nodel betwece the allocation of labse. How does the firm value it intluesce the allocation? (d) Describe the transuission of a 1% techaology shock in this mosel, cotnparing with that of a standard real businese cycle inodel. (c) Many of the variables in this teodel, including C1, th, 1 and 0 are in units of the consumption basket, which lus an associated price index P1. Explain why we tmist deflate vuriables by a data-coasistent price index to coarpare with the data. What transformation do we apply? Suppose we introduce plysical eital in the BGM model as folkows. The production function becotmes M=Z1h8l11a. (Note, inlike the decture notex we let a be the capital share). Capital ascumulatioe catiofies Kt+1=(1t)Kt+It for deprexiation rate x(0,1). Houscholds necuminlate capital and rent it to firms at rate re - (f) What is the new household budget constraint in the model? What is the Euler cquation with respect to plysical capital? (g) Aggregate the btalget contraint over hotseholds and we the marbet clesing condition x1=1 - the m of shares equals uaity-to obtain the new ngeresate resource constraint. What to the form of aggregate investment TIx ? 1. Endogenous entry, product variety, and business cycles The baseline model of Ballicie, Glitroni, and Melitz (2012) uader constant-elasticity-of substitution can be written is the following system: pr=c1Ztwr pt=Nt1/(s1) d1=c11C1/Ni vr=wrZtfE Nt=(1)(Nt1+Nt,t1) xR13/=Ciwk x=(1d)Et{Ci+1C1(d1+1+v2+1)} Ct+NC1d1vt=wtLt+Nit logZ1=klogZr1+ct,t,r,1N(0,2) (a) Carefully explain each variable, interpet each cquation, and point out the ingredjents which differ from the real business cycle model. (b) What are the state variables (endogenotes and exogenons)? What are the control variables? (c) What is the quantity of labor employed in product developtuent LtE?. Describe the tradooff in the nodel betwece the allocation of labse. How does the firm value it intluesce the allocation? (d) Describe the transuission of a 1% techaology shock in this mosel, cotnparing with that of a standard real businese cycle inodel. (c) Many of the variables in this teodel, including C1, th, 1 and 0 are in units of the consumption basket, which lus an associated price index P1. Explain why we tmist deflate vuriables by a data-coasistent price index to coarpare with the data. What transformation do we apply? Suppose we introduce plysical eital in the BGM model as folkows. The production function becotmes M=Z1h8l11a. (Note, inlike the decture notex we let a be the capital share). Capital ascumulatioe catiofies Kt+1=(1t)Kt+It for deprexiation rate x(0,1). Houscholds necuminlate capital and rent it to firms at rate re - (f) What is the new household budget constraint in the model? What is the Euler cquation with respect to plysical capital? (g) Aggregate the btalget contraint over hotseholds and we the marbet clesing condition x1=1 - the m of shares equals uaity-to obtain the new ngeresate resource constraint. What to the form of aggregate investment TIx