Explain the microeconomics foundations of the Real Business Cycle model,and the modern DSGE approach to studying economic fluctuations.

Explain the microeconomics foundations of the Real Business Cycle model,and the modern DSGE approach to studying economic fluctuations.The equilibrium of the DSGE model is characterised by the following equations.Constraints:𝑌𝑡=𝐶𝑡+𝐼𝑡𝐾𝑡+1=𝐼𝑡+(1−𝛿)𝐾𝑡𝑌𝑡=𝐴𝑡𝐹(𝐾𝑡,𝑁𝑡)ln𝐴𝑡=𝜓ln𝐴𝑡−1+𝜀𝑡Firms:𝐴𝑡𝐹𝐾(𝐾𝑡,𝑁𝑡)=𝑟𝑡+𝛿=𝑅𝑡⇒𝐾𝑡𝑑=𝐾𝑡𝑑(𝐴𝑡,𝑁𝑡)𝐴𝑡𝐹𝑁(𝐾𝑡,𝑁𝑡)=𝑊𝑡⇒𝑁𝑡𝑑=𝑁𝑡𝑑(𝑊𝑡,𝐴𝑡,𝐾𝑡)Households:𝑢𝐶𝑡(𝐶𝑡,1−𝑁𝑡)=𝛽𝐸𝑡[(1+𝑟𝑡+1)𝑢𝐶𝑡+1(𝐶𝑡+1,1−𝑁𝑡+1)]𝑢𝑁𝑡(𝐶𝑡,1−𝑁𝑡)=𝑢𝐶𝑡(𝐶𝑡,1−𝑁𝑡)𝑊𝑡⇒𝑁𝑡𝑠=𝑁𝑡𝑠(𝑊𝑡,𝐶𝑡)Explain and use these equations to describe an economic cycle triggered by a persistent shock to total factor productivity(TFP). In as much detail as possible explain how the model can be used to generate the statistics of an artificial cycle and how the stylized facts of real world fluctuations are obtained. Discuss how successful the model is at matching the stylized facts.