Under current conditions it costs $10 per hour to hire labor while capital costs $100 per...

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Under current conditions it costs $10 per hour to hire labor while capital costs $100 per hour to employ. Also assume that your firm's production function is given by the following: Q=18K1 a. Write out the marginal product of capital and the marginal product of labor functions. Do the same for the average product functions. b. In the short-run situation your output can be varied only by changing the amount of labor you employ. If you are currently using 16 units of capital, what happens to the marginal product of labor as you use more labor to expand your output? c. Now rather than capital being fixed (let capital be K in your MPI function), what happens to the marginal product of labor if capital is increased? Why does changing your capital utilization affect the marginal productivity of your labor input? d. Suppose you wanted to make use of the production relationship and forecast how many workers you would need to hire (L) to produce a given level of output (Q) instead of the current relationship which tells you how much output you can produce (Q) with a given amount of labor (L). Assume as in part b that you are making a short-run determination with capital fixed at 16 units. (The expression here can get a bit messy, so you don't have to simplify your result completely. I am looking for the ability to construct the proper expression.) e. We know that the total cost of producing some level of output for this firm is just the cost of the inputs required to produce the output. On a general level this is just given by TC=wL+ rK. As managers however, we often want to know cost per unit produced (in other words, costs as a function of output) not cost per until of labor or capital hired. Using the relationship your derived in part "d" that relates labor to output, substitute that information into the total cost expression to find the total cost function of the firm as a function of quantity produced. (Again, I am looking for the ability to construct the expression, so you don't need to completely simplify the result.) Under current conditions it costs $10 per hour to hire labor while capital costs $100 per hour to employ. Also assume that your firm's production function is given by the following: Q=18K1 a. Write out the marginal product of capital and the marginal product of labor functions. Do the same for the average product functions. b. In the short-run situation your output can be varied only by changing the amount of labor you employ. If you are currently using 16 units of capital, what happens to the marginal product of labor as you use more labor to expand your output? c. Now rather than capital being fixed (let capital be K in your MPI function), what happens to the marginal product of labor if capital is increased? Why does changing your capital utilization affect the marginal productivity of your labor input? d. Suppose you wanted to make use of the production relationship and forecast how many workers you would need to hire (L) to produce a given level of output (Q) instead of the current relationship which tells you how much output you can produce (Q) with a given amount of labor (L). Assume as in part b that you are making a short-run determination with capital fixed at 16 units. (The expression here can get a bit messy, so you don't have to simplify your result completely. I am looking for the ability to construct the proper expression.) e. We know that the total cost of producing some level of output for this firm is just the cost of the inputs required to produce the output. On a general level this is just given by TC=wL+ rK. As managers however, we often want to know cost per unit produced (in other words, costs as a function of output) not cost per until of labor or capital hired. Using the relationship your derived in part "d" that relates labor to output, substitute that information into the total cost expression to find the total cost function of the firm as a function of quantity produced. (Again, I am looking for the ability to construct the expression, so you don't need to completely simplify the result.)

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a Marginal Product of Capital MPK MPK QK 54K2L3 Marginal Product of Labor MPL MPL QL 54K3L2 Average ... View the full answer