Precise and correct.

The Romer model can be described by 4 equations: Yt = AtLy,t AAtti = ZAtLa,t GONE Ly,t + Lat = L La,t = IL where Y is final output, A is ideas/knowledge, Ly is employment in production of final out- put, La is the number of researchers, and L is the population. i What are the endogenous variables? What are the exogenous variables and the pa- rameters? ( 5 points)Let W (t) be a zero mean white Gaussian noise process with power spectral density No/2 Watts/Hz. Define Zi = _ W(t);(t)dt, i = 1, 2, where 1(t) and 42(t) are orthonormal on (-oo, co). Use the results from Section 3.8.1 to answer the following questions. a) What is the variance of Z1? Denote this variance by of. b) What is the variance of Y = Z1 + Z2? Denote this variance by of. c) Find the pdf of Y.7. A monopolist retires and hands her company over to her two children. The children have an argument and decide they cannot work together, and split the company into two- Firm 1 and Firm 2. Each firm can choose to produce a high level of output, or a low level of output. For each scenario, Firm I's profits are written in the lower left corner of the cells, while Firm 2's profits are written in the upper right corner of the cells. Firm 2 High Output Low Output High Output $1.600 $1,500 $1.600 $2.000 Firm 1 $2,000 Low Output $1,800 $1,500 $1,800 a. Explain why both firms producing "Low Output" gives higher profits to each firm than both firms producing "High Output". (Recall: the two firms are the only sellers in the market.) b. Explain why each firm would have an incentive to "cheat" on an agreement to keep production low