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Question 1. (15 points) A company operates with the following production function: q = 20L*K? 512K + 2L%5K a. (3 points) What is its short-run production function if capital is fixed at K=10? b. (6 points) What are the firm's marginal product of labour and average product of labour in the short run when K=10? c. (6 points) Show that the firm's elasticity of output with respect to labour in the short run is a function of marginal product of labour and average product of labour for any value of K. Calculate the short-run elasticity of output with respect to labour when K=10. Question 2 (14 points) : Sam and Alex are managers at a technology firm trying to optimize their project outputs. Their output depends on the number of hours spent on software development, D, and the number of hours spent on market analysis, M. Specifically, Sam's project output function is P, = 3D%*M%_ and Alex's project output function is P, = 3 DU.S MU.S ; (a) (7 points) Calculate the marginal productivity of dedicating additional hours to market analysis for both Sam and Alex. (b) (7 points) Determine the marginal rate of technical substitution (MRTS) between software development and market analysis for both Sam and Alex