IV. A firm's production function is given by q = (L0.5K0.5)2 for L > 0 and K > 0, where q is quantity of output, L is amount of labor employed, and K is the amount of capital used. 1. Suppose that both L and K change by the same proportion > 1. What is the proportion change in output q? Show how you arrived at your answer. 2. Does this production function exhibit increasing, decreasing, or constant returns to scale? Show how you arrive at your answer. 3. Is the marginal product of labor ever diminishing for this production function? If so, when? If not why not? Use calculus and words to answer this question. 4. Is the marginal product of capital ever diminishing for this production function? If so, when? If not why not? Use calculus and words to answer this question. 5. What is the marginal rate of technical substitution of L for K for this production function? Simplify your answer. 8. Find the derivative that determines what happens to this firm's marginal rate of technical substitution between labor and capital as the firm uses more labor and less capital along any given isoquant. Simplify your answer. Evaluate the sign of this derivative for all values of L>0 and K> 0 then interpret the sign. 6. When the firm use 16 units of labor and 4 units of capital, what are the (a) output elasticity of labor and (b) output elasticity of capital? 7. Find the elasticity of substitution for this production function and show that it is a constant for all values of L and K.