please explain as well
please explian as well
please explian as well
2. CASE STUDY (This case study is adapted from one written by Mike Price. We will contime it in the Week 5 written homework.) The Cobb-Douglas model relates a company's production output to the amount of labor (worker hours) and capital (machines, etc) it uses. The model was originally based on empirical observations, though there are now also some conceptual justifications for it. It is also used at the scale of economic sectors or entire economies. The model will come up again in the third part of the class project. (Advantages of this model include that it's simple to use and tends to fit or predict data surprisingly well.) INSTRUCTOR: ROBERT LIPSHITZ The Cobb-Douglas production function for a company building widgets is given by Y = ALAK- where Y is the total number of widgets produoed, L is the number of units of labor (in hours, for instance), and K is the amount of capital invested in equipment and so on (in dollars, for instance). Both A and B are constants (real numbers), which depend on what company is being modeled. The constant 3 is between 0 and 1. The constants A and 8 are typically found by fitting the equation to past data. Below, you will study an imaginary company where is the following. The blank spot - in the table below is the last digit of your student ID. If your discussion section is with Cruz Godar use 8 = 0.4+0.0_ Elisha Hulbert use 3 -0.5 +0.0 Jacob Lebovic use 8 = 0.6 +0.0_ Bo Phillips use 3 = 0.7 +0.0_ Aaron Victorin-Vangerud use 3 = 0.8 +0.0 For example, if my ID were 951234567 and my discussion section were with Jacob Lebovic then I would use 8 = 0.67. We will consider a company with the following numbers for 2019: Annual labor of 20 million hours (which corresponds to about 10,000 full-time work- ers), . Capital investment of 100 million dollars, and . Annual output of 1 million widgets. (a) What is your value of S? (b) Use the data above and the Cobb-Douglas production function to compute A to five decimal places (c) Assume that the total output of the company is fixed at 1 million widgets (ie, Y = 1000000). Use the value of A you found in the previous part to write the Cobb-Douglas production equation only in terms of L and K. (d) Solve the equation you found above for K as a function of L. 1.c., as K = f(L). (Hint: you will need to use rules of exponents. Your answer should be of the form f(L) = cL for some constants c and d.) (e) Using the function from the previous part, compute "(L). (This is called the marginal rate of technical substitution.) What does the fact that f'(L) is always negative imply about labor and capital? (Re- member that we are assuming the total output is constant.) (One or two sentences.) (g) Compute and write a sentence or two interpreting the value of f'(18000000) = f'(18x 10%). Include units in your computation and sentence. 2. CASE STUDY (This case study is adapted from one written by Mike Price. We will continue it in the Week 5 written homework.) The Cobb-Douglas model relates a company's production output to the amount of labor (worker hours) and capital (machines, etc) it uses. The model was originally based on empirical observations, though there are now also some conceptual justifications for it. It is also used at the scale of economic sectors or entire economies. The model will come up again in the third part of the class project. (Advantages of this model include that it's simple to use and tends to fit or predict data surprisingly well.) 1 2 INSTRUCTOR: ROBERT LIPSHITZ The Cobb-Douglas production function for a company building widgets is given by Y = ALR1-8 where Y is the total number of widgets produced, L is the number of units of labor (in hours, for instance), and K is the amount of capital invested in equipment and so on (in dollars, for instance). Both A and B are constants (real numbers), which depend on what company is being modeled. The constant 8 is between 0 and 1. The constants A and 8 are typically found by fitting the equation to past data. are constans Team members), WC depend on what company is being modeled. The constant B is between 0 and 1. The constants A and B are typically found by fitting the equation to past data. Below, you will study an imaginary company where is the following. The blank spot in the table below is the last digit of your student ID. If your discussion section is with Cruz Godar use = 0.4+0.0_ Elisha Hulbert use B = 0.5 +0.0 Jacob Lebovic use B = 0.6 + 0.0 Bo Phillips use B = 0.7 +0.0_ Aaron Victorin-Vangerud use 8 = 0.8 +0.0_. For example, if my ID were 951234567 and my discussion section were with Jacob Lebovic then I would use B = 0.67. We will consider a company with the following numbers for 2019: Annual labor of 20 million hours (which corresponds to about 10,000 full-time work- ers), . Capital investment of 100 million dollars, and Annual output of 1 million widgets. (a) What is your value of B? (b) Use the data above and the Cobb-Douglas production function to compute A to five decimal places (c) Assume that the total output of the company is fixed at 1 million widgets (i.e., 1000000). Use the value of A you found in the previous part to write the Cobb-Douglas production equation only in terms of and R (d) Solve the equation you found above for K as a function of L, i.e., as K f(L) (Hint: you will need to use rules of exponents. Your answer should be of the form S(L) = cL" for some constants c and d.) (e) Using the function from the previous part, compute l'(L). (This is called the marginal rate of technical substitution.) (f) What does the fact that f'(L) is always negative imply about labor and capital? (Re- member that we are assuming the total output is constant.) (One or two sentences) ($) Compute and write a sentence or two interpreting the value of l' (18000000) = f'(18 x 10%). Include units in your computation and sentence, Y = 2. CASE STUDY (This case study is adapted from one written by Mike Price. We will continue it in the Week 5 written homework.) The Cobb-Douglas model relates a company's production output to the amount of labor (worker hours) and capital (machines, etc) it uses. The model was originally based on empirical observations, though there are now also some conceptual justifications for it. It is also used at the scale of economic sectors or entire economies. The model will come up again in the third part of the class project. (Advantages of this model include that it's simple to use and tends to fit or predict data surprisingly well.) 2 INSTRUCTOR: ROBERT LIPSHITZ The Cobb-Douglas production function for a company building widgets is given by Y = ALPR- where Y is the total number of widgets produced, L is the number of units of labor (in hours, for instance). and K is the amount of capital invested in equipment and so on (in dollars, for instance). Both A and B are constants (real numbers), which depend on what company is being modeled. The constant 3 is between 0 and 1. The constants A and B are typically found by fitting the equation to past data. Below, you will study an imaginary company where 3 is the following. The blank spot in the table below is the last digit of your student ID. If your discussion section is with Cruz Godar use B = 0.0.0 Elisha Hulbert 1 3 =0.5 +0.0 Jacob Lebovic ulse 8 = 0.6 0.0 Bo Phillips use = 0.7 0.0 in the table below is the last digit of your student ID. If your discussion section is with Cruz Godar use B = 0.4 +0.0__ Elisha Hulbert use B = 0.5 + 0.0 Jacob Lebovic use B=0.6 + 0.0 Bo Phillips use B = 0.7 + 0.0 Aaron Victorin-Vangerud use B = 0.8 +0.0_ For example, if my ID were 951234567 and my discussion section were with Jacob Lebovic then I would use B = 0.67. We will consider a company with the following numbers for 2019: Annual labor of 20 million hours (which corresponds to about 10,000 full-time work- ers), Capital investment of 100 million dollars, and Annual output of 1 million widgets. (a) What is your value of B? (b) Use the data above and the Cobb-Douglas production function to compute A to five decimal places. (c) Assume that the total output of the company is fixed at 1 million widgets (i.e., Y 1000000). Use the value of A you found in the previous part to write the Cobb-Douglas production equation only in terms of L and K. (d) Solve the equation you found above for K as a function of L, i.e., as K f(L). (Hint: you will need to use rules of exponents. Your answer should be of the form f(L) = cL for some constants c and d.) (e) Using the function f from the previous part, compute f'(L). (This is called the marginal rate of technical substitution.) (f) What does the fact that l'(L) is always negative imply about labor and capital? (Re- member that we are assuming the total output is constant.) (One or two sentences) (8) Compute and write a sentence or two interpreting the value of f'(18000000) = f'(18x 10%). Include units in your computation and sentence. 2. CASE STUDY (This case study is adapted from one written by Mike Price. We will contime it in the Week 5 written homework.) The Cobb-Douglas model relates a company's production output to the amount of labor (worker hours) and capital (machines, etc) it uses. The model was originally based on empirical observations, though there are now also some conceptual justifications for it. It is also used at the scale of economic sectors or entire economies. The model will come up again in the third part of the class project. (Advantages of this model include that it's simple to use and tends to fit or predict data surprisingly well.) INSTRUCTOR: ROBERT LIPSHITZ The Cobb-Douglas production function for a company building widgets is given by Y = ALAK- where Y is the total number of widgets produoed, L is the number of units of labor (in hours, for instance), and K is the amount of capital invested in equipment and so on (in dollars, for instance). Both A and B are constants (real numbers), which depend on what company is being modeled. The constant 3 is between 0 and 1. The constants A and 8 are typically found by fitting the equation to past data. Below, you will study an imaginary company where is the following. The blank spot - in the table below is the last digit of your student ID. If your discussion section is with Cruz Godar use 8 = 0.4+0.0_ Elisha Hulbert use 3 -0.5 +0.0 Jacob Lebovic use 8 = 0.6 +0.0_ Bo Phillips use 3 = 0.7 +0.0_ Aaron Victorin-Vangerud use 3 = 0.8 +0.0 For example, if my ID were 951234567 and my discussion section were with Jacob Lebovic then I would use 8 = 0.67. We will consider a company with the following numbers for 2019: Annual labor of 20 million hours (which corresponds to about 10,000 full-time work- ers), . Capital investment of 100 million dollars, and . Annual output of 1 million widgets. (a) What is your value of S? (b) Use the data above and the Cobb-Douglas production function to compute A to five decimal places (c) Assume that the total output of the company is fixed at 1 million widgets (ie, Y = 1000000). Use the value of A you found in the previous part to write the Cobb-Douglas production equation only in terms of L and K. (d) Solve the equation you found above for K as a function of L. 1.c., as K = f(L). (Hint: you will need to use rules of exponents. Your answer should be of the form f(L) = cL for some constants c and d.) (e) Using the function from the previous part, compute "(L). (This is called the marginal rate of technical substitution.) What does the fact that f'(L) is always negative imply about labor and capital? (Re- member that we are assuming the total output is constant.) (One or two sentences.) (g) Compute and write a sentence or two interpreting the value of f'(18000000) = f'(18x 10%). Include units in your computation and sentence. 2. CASE STUDY (This case study is adapted from one written by Mike Price. We will continue it in the Week 5 written homework.) The Cobb-Douglas model relates a company's production output to the amount of labor (worker hours) and capital (machines, etc) it uses. The model was originally based on empirical observations, though there are now also some conceptual justifications for it. It is also used at the scale of economic sectors or entire economies. The model will come up again in the third part of the class project. (Advantages of this model include that it's simple to use and tends to fit or predict data surprisingly well.) 1 2 INSTRUCTOR: ROBERT LIPSHITZ The Cobb-Douglas production function for a company building widgets is given by Y = ALR1-8 where Y is the total number of widgets produced, L is the number of units of labor (in hours, for instance), and K is the amount of capital invested in equipment and so on (in dollars, for instance). Both A and B are constants (real numbers), which depend on what company is being modeled. The constant 8 is between 0 and 1. The constants A and 8 are typically found by fitting the equation to past data. are constans Team members), WC depend on what company is being modeled. The constant B is between 0 and 1. The constants A and B are typically found by fitting the equation to past data. Below, you will study an imaginary company where is the following. The blank spot in the table below is the last digit of your student ID. If your discussion section is with Cruz Godar use = 0.4+0.0_ Elisha Hulbert use B = 0.5 +0.0 Jacob Lebovic use B = 0.6 + 0.0 Bo Phillips use B = 0.7 +0.0_ Aaron Victorin-Vangerud use 8 = 0.8 +0.0_. For example, if my ID were 951234567 and my discussion section were with Jacob Lebovic then I would use B = 0.67. We will consider a company with the following numbers for 2019: Annual labor of 20 million hours (which corresponds to about 10,000 full-time work- ers), . Capital investment of 100 million dollars, and Annual output of 1 million widgets. (a) What is your value of B? (b) Use the data above and the Cobb-Douglas production function to compute A to five decimal places (c) Assume that the total output of the company is fixed at 1 million widgets (i.e., 1000000). Use the value of A you found in the previous part to write the Cobb-Douglas production equation only in terms of and R (d) Solve the equation you found above for K as a function of L, i.e., as K f(L) (Hint: you will need to use rules of exponents. Your answer should be of the form S(L) = cL" for some constants c and d.) (e) Using the function from the previous part, compute l'(L). (This is called the marginal rate of technical substitution.) (f) What does the fact that f'(L) is always negative imply about labor and capital? (Re- member that we are assuming the total output is constant.) (One or two sentences) ($) Compute and write a sentence or two interpreting the value of l' (18000000) = f'(18 x 10%). Include units in your computation and sentence, Y = 2. CASE STUDY (This case study is adapted from one written by Mike Price. We will continue it in the Week 5 written homework.) The Cobb-Douglas model relates a company's production output to the amount of labor (worker hours) and capital (machines, etc) it uses. The model was originally based on empirical observations, though there are now also some conceptual justifications for it. It is also used at the scale of economic sectors or entire economies. The model will come up again in the third part of the class project. (Advantages of this model include that it's simple to use and tends to fit or predict data surprisingly well.) 2 INSTRUCTOR: ROBERT LIPSHITZ The Cobb-Douglas production function for a company building widgets is given by Y = ALPR- where Y is the total number of widgets produced, L is the number of units of labor (in hours, for instance). and K is the amount of capital invested in equipment and so on (in dollars, for instance). Both A and B are constants (real numbers), which depend on what company is being modeled. The constant 3 is between 0 and 1. The constants A and B are typically found by fitting the equation to past data. Below, you will study an imaginary company where 3 is the following. The blank spot in the table below is the last digit of your student ID. If your discussion section is with Cruz Godar use B = 0.0.0 Elisha Hulbert 1 3 =0.5 +0.0 Jacob Lebovic ulse 8 = 0.6 0.0 Bo Phillips use = 0.7 0.0 in the table below is the last digit of your student ID. If your discussion section is with Cruz Godar use B = 0.4 +0.0__ Elisha Hulbert use B = 0.5 + 0.0 Jacob Lebovic use B=0.6 + 0.0 Bo Phillips use B = 0.7 + 0.0 Aaron Victorin-Vangerud use B = 0.8 +0.0_ For example, if my ID were 951234567 and my discussion section were with Jacob Lebovic then I would use B = 0.67. We will consider a company with the following numbers for 2019: Annual labor of 20 million hours (which corresponds to about 10,000 full-time work- ers), Capital investment of 100 million dollars, and Annual output of 1 million widgets. (a) What is your value of B? (b) Use the data above and the Cobb-Douglas production function to compute A to five decimal places. (c) Assume that the total output of the company is fixed at 1 million widgets (i.e., Y 1000000). Use the value of A you found in the previous part to write the Cobb-Douglas production equation only in terms of L and K. (d) Solve the equation you found above for K as a function of L, i.e., as K f(L). (Hint: you will need to use rules of exponents. Your answer should be of the form f(L) = cL for some constants c and d.) (e) Using the function f from the previous part, compute f'(L). (This is called the marginal rate of technical substitution.) (f) What does the fact that l'(L) is always negative imply about labor and capital? (Re- member that we are assuming the total output is constant.) (One or two sentences) (8) Compute and write a sentence or two interpreting the value of f'(18000000) = f'(18x 10%). Include units in your computation and sentence
