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Problem 1A (40 points) According to the new classical investment model we have: Pk MPK = P (r + 8 ) (1) Derive the above equation and explain it briefly. ii. Suppose that a firm has a production function of Y = AK0.5L 0.5 where Y is output, A is productivity (or technology), K is capital and L is labour. When A = 2, K = 100 and L = 400. Obtain the marginal product of capital (MPK). iii. Consider a production function that Y = AKL, where A = 0.1, L = 1, Pk =1, P = 1, r= 0.1, and 8=0.1. What is the optimal level of capital, K*, in the steady state