Explain the microeconomic foundations of the Real Business Cycle model,and the modernDSGEapproach to studying economic fluctuations.

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3.Explain the microeconomic foundations of the Real Business Cycle model,and the modernDSGEapproach to studying economic fluctuations.The equilibrium of the DSGE model is characterisedby the following equations.Constraints:π‘Œπ‘‘=𝐢𝑑+𝐼𝑑𝐾𝑑+1=𝐼𝑑+(1βˆ’π›Ώ)πΎπ‘‘π‘Œπ‘‘=𝐴𝑑𝐹(𝐾𝑑,𝑁𝑑)ln𝐴𝑑=πœ“lnπ΄π‘‘βˆ’1+πœ€π‘‘Firms:𝐴𝑑𝐹𝐾(𝐾𝑑,𝑁𝑑)=π‘Ÿπ‘‘+𝛿=𝑅𝑑⇒𝐾𝑑𝑑=𝐾𝑑𝑑(𝐴𝑑,𝑁𝑑)𝐴𝑑𝐹𝑁(𝐾𝑑,𝑁𝑑)=π‘Šπ‘‘β‡’π‘π‘‘π‘‘=𝑁𝑑𝑑(π‘Šπ‘‘,𝐴𝑑,𝐾𝑑)Households:𝑒𝐢𝑑(𝐢𝑑,1βˆ’π‘π‘‘)=𝛽𝐸𝑑[(1+π‘Ÿπ‘‘+1)𝑒𝐢𝑑+1(𝐢𝑑+1,1βˆ’π‘π‘‘+1)]𝑒𝑁𝑑(𝐢𝑑,1βˆ’π‘π‘‘)=𝑒𝐢𝑑(𝐢𝑑,1βˆ’π‘π‘‘)π‘Šπ‘‘β‡’π‘π‘‘π‘ =𝑁𝑑𝑠(π‘Šπ‘‘,𝐢𝑑)

Explain and use these equations to describe an economic cycle triggered by a persistent shock to totalfactor productivity(TFP). In as much detail as possible explain how the model can be used to generate thestatisticsof an artificial cycle and how the stylised facts of real world fluctuationsare obtained. Discuss howsuccessful themodel is at matching the stylised facts.