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A profit maximising firm uses capital K to produce output according to the following production...

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Finance

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A profit maximising firm uses capital K to produce output according to the following production function Q(K)= ({K ak2) where a is a positive constant, and sells output at a given price of p. The cost of investment is bi?, where b is a positive constant and I represents investment. The firm maximises profits in continuous time beginning from time t = 0 to time t =T, subject to the differential equation governing capital, K = I SK, where d is a known rate of depreciation and K(0) = Ko . (a) Identify the control and state variables and set up the maximisation problem (b) Solve the maximisation problem for the control, state and co-state variables. After obtaining the FOC, solve the required pair of differential equations using the direct method. Express your solutions in terms of the constants G,C2 , roots 7, 72 and the particular solutions a and K

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