(25 Points) 1. (a) Explain the role of the business manager in the production process. (b)...

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(25 Points) 1. (a) Explain the role of the business manager in the production process. (b) The "classical" production function is depicted in Figure 5-1 on p. 141 (Bayes, 10e) of your textbook with three (3) stages of production that are demarcated by the vertical lines in the diagram. Specifically, Stage I of production is the range of the variable input usage up to the first vertical line (variable input usage between the y- axis and the first vertical line) in Figure 5-1; Stage II is the range of variable input usage from the first vertical line to the second vertical line in Figure 5-1 (the middle section of the graph); and State III is the range of variable input usage beyond State II (variable input usage beyond the middle section of Fig. 5-1). Carefully describe the characteristics of Stage II of the classical production function with regard to Total Product, Marginal Product, and Average Product of the variable input, labor. (c) Explain why Stage II is considered the rational stage of production. (d) Briefly discuss two major limitations of the Leontief production function in comparison with the Cobb-Douglas production function. (25 Points) 2. (a) Clearly state and explain the condition for cost-minimizing use of labor and capital in a production process, where labor and capital are variable inputs. (b) Graphically illustrate (manually drawn graph) and explain why the stated condition in (a) is true. (c) Suppose you manage a firm with the production function Q = F(K, L) = 4K + 8L, and you are able to hire labor at $60 per hour and your rental rate on capital is $20 per hour. Show your steps and calculations to determine the cost- minimizing capital (K) and labor (L) mix to produce 32 units of output (Q). (d) Provide a graphical illustration (manually drawn graph) to justify your answer in (c). (25 Points) 3. Suppose that you are the manager of Albany Blenders, Inc., a manufacturer of high-tech blenders, and you believe your production process is approximated by the Cobb-Douglass production function, Q = akb Lc, where Q is your firm's output, K is capital, and L is labor. You have carefully collected data on your firm's output, capital, and labor as provided on the attached Excel Spreadsheet in GaView. a. With Microsoft Excel, use the data provided to estimate the Cobb-Douglas production function of your firm. Upload an Excel file containing the Excel Worksheet of your estimated production function and, with your regression analysis, write the equation of your estimated Cobb-Douglas production function in 2 decimal points. b. With your Excel Worksheet (regression analysis results), show your steps and calculations to determine the cost- minimizing combination of labor and capital for producing 5,000 units of output if labor costs $85.50 per unit and capital costs $118.75 per unit. c. Graphically illustrate and carefully discuss the relationships among marginal cost, average variable cost, average total cost, and average fixed cost, when a firm could produce any level of output. (25 Points) 4. Suppose a firm's multiproduct cost function is C(Q1, Q2) = 65 - 0.5Q1 Q2 +0.30 + 0.402, and management wishes to produce 12 units of each product (Q = Q = 12 units). (a) Determine the marginal cost of each product at the planned levels of production. Clearly show your steps and calculations. (b) Clearly show your steps and calculate the total cost of producing Q1 and Q2 jointly at one plant and the total cost of producing Q1 and Q2 separately at two independent plants at the planned levels of production. What is the economic relevance of this analysis? Explain. (c) Clearly show your steps and estimate the impact of an increase in the production of one product on the marginal cost of the other product at the planned production level. What is the economic relevance of this analysis? Explain. ....end.... (25 Points) 1. (a) Explain the role of the business manager in the production process. (b) The "classical" production function is depicted in Figure 5-1 on p. 141 (Bayes, 10e) of your textbook with three (3) stages of production that are demarcated by the vertical lines in the diagram. Specifically, Stage I of production is the range of the variable input usage up to the first vertical line (variable input usage between the y- axis and the first vertical line) in Figure 5-1; Stage II is the range of variable input usage from the first vertical line to the second vertical line in Figure 5-1 (the middle section of the graph); and State III is the range of variable input usage beyond State II (variable input usage beyond the middle section of Fig. 5-1). Carefully describe the characteristics of Stage II of the classical production function with regard to Total Product, Marginal Product, and Average Product of the variable input, labor. (c) Explain why Stage II is considered the rational stage of production. (d) Briefly discuss two major limitations of the Leontief production function in comparison with the Cobb-Douglas production function. (25 Points) 2. (a) Clearly state and explain the condition for cost-minimizing use of labor and capital in a production process, where labor and capital are variable inputs. (b) Graphically illustrate (manually drawn graph) and explain why the stated condition in (a) is true. (c) Suppose you manage a firm with the production function Q = F(K, L) = 4K + 8L, and you are able to hire labor at $60 per hour and your rental rate on capital is $20 per hour. Show your steps and calculations to determine the cost- minimizing capital (K) and labor (L) mix to produce 32 units of output (Q). (d) Provide a graphical illustration (manually drawn graph) to justify your answer in (c). (25 Points) 3. Suppose that you are the manager of Albany Blenders, Inc., a manufacturer of high-tech blenders, and you believe your production process is approximated by the Cobb-Douglass production function, Q = akb Lc, where Q is your firm's output, K is capital, and L is labor. You have carefully collected data on your firm's output, capital, and labor as provided on the attached Excel Spreadsheet in GaView. a. With Microsoft Excel, use the data provided to estimate the Cobb-Douglas production function of your firm. Upload an Excel file containing the Excel Worksheet of your estimated production function and, with your regression analysis, write the equation of your estimated Cobb-Douglas production function in 2 decimal points. b. With your Excel Worksheet (regression analysis results), show your steps and calculations to determine the cost- minimizing combination of labor and capital for producing 5,000 units of output if labor costs $85.50 per unit and capital costs $118.75 per unit. c. Graphically illustrate and carefully discuss the relationships among marginal cost, average variable cost, average total cost, and average fixed cost, when a firm could produce any level of output. (25 Points) 4. Suppose a firm's multiproduct cost function is C(Q1, Q2) = 65 - 0.5Q1 Q2 +0.30 + 0.402, and management wishes to produce 12 units of each product (Q = Q = 12 units). (a) Determine the marginal cost of each product at the planned levels of production. Clearly show your steps and calculations. (b) Clearly show your steps and calculate the total cost of producing Q1 and Q2 jointly at one plant and the total cost of producing Q1 and Q2 separately at two independent plants at the planned levels of production. What is the economic relevance of this analysis? Explain. (c) Clearly show your steps and estimate the impact of an increase in the production of one product on the marginal cost of the other product at the planned production level. What is the economic relevance of this analysis? Explain. ....end....