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Let the production of a particular good for a certain firm be described by the production function F(K,L) = 30K2/321/3

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Let the production of a particular good for a certain firm be described by the production function F(K,L) = 30K2/321/3. Solve for the following: 1. Determine the degree of homogeneity of the production function. Does it exhibit constant returns to scale? Explain your answer. 2. Derive the marginal product of capital and labor functions, Fx(K,L) and F_(K,L) respectively. 3. Suppose that the firm has installed 5 units of capital and has hired 8 laborers. If the firm has decided to hire one more laborer, how many additional units of the product will the 9th laborer be able to contribute to the firm's production? 4. Determine whether the given production function obeys the law of diminishing marginal product. That is, regardless of the values for K and L, the second order partial derivatives FKK(K, L) and FLL(K,L) are always going to be a negative expression.