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- PS3 (3) Question: (i) What does a MRTS = 4 mean? (ii) Explain the term "Marginal Rate of Technical Substitution"?Marty's frozen yogurt shop sells cups of frozen yogurt in a local university town. He owns 3 frozen yogurt machines. His other inputs are refrigerators, frozen yogurt mix, cups, sprinkles, and workers. He estimates that his production function when he increases the number of workers (and materials like yoghurt mix and cups) is: Quantity of Quantity of workers frozen (labor) yoghurt (cups) 1 110 200 3 270 300 320 6. 330 a) What are the fixed inputs and what are the variable inputs in this production process? b) What is Marty's VC and TC when he produces 110 cups? Assume he pays each worker $80 a day. His fixed costs are $100 a day. Other VC come to $.50 per cup of yogurt produced. Calculate the VC, FC and TC for all levels of output. c) Calculate MC for all levels of output. Page: 4Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by the following function. S- 20100.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min s.t. -55,000 L.C20 (b) Solve the optimization problem you formulated in part (a). (Hnt: When using Excel Solver, start with an initial L>O and Co. Round your answers to the nearest integer.) at (L. C) =
- Mr. Diddy grows and sells Pineapple. His company is named "Do it Diddy Way!!" Suppose that to produce Pineapple, two inputs are required. 1. Land (size of land) 2. Workers (number of workers) Diddy has 1.5 acres of land inherited from his late Daddy and he uses the inherited land to produce pineapple. His company's production function (per day) table is shown below: Quantity of pineapple number of workers 0 0 5 1 20 2 40 3 70 4 140 5 180 6 195 7 200 8 203 9 Answer the following questions: 1. Is the production considered a short-run or long-run? What is a fixed input? What is a variable input? 2. Draw the total product curve (output on the vertical axis and workers on the horizontal axis) Draw the MPL curve (MPL on the vertical axis and workers on the horizontal axis) 3. 4. What is the quantity of pineapple per day when Diddy hires7 workers? What is the MPL of the 7th worker? 5. After how many workers used does the MPL start to diminish. 6. Suppose that the market price of pineapple is…A company produces children's toys. The manager noticed the connection between the number of employed workers and the quantity of toys produced per month, which are presented in the table of following: a) In what period is this firm operating? Why? b) What is the average product when 5 workers are employed? c) What is the marginal product when 7 workers are employed? What does this value mean? d) Does the law of declining marginal income apply? If yes to which worker? e) In this production function do we have total declining revenues? If so, which worker happens? f) Graph the curves of total product (TP), marginal product (MP) and product average (AP).A commercial fisherman notices the following relationship between hours spent fishing and the quantity of fish caught: Hours Quantity of Fish (Pounds) 0 0 1 10 2 19 3 25 4 27 5 28 Complete the following table with the marginal product of each hour spent fishing. Hours Quantity of Fish Marginal Product (Pounds) (Pounds) 0 0 10 1 10 9 2 19 6 3 25 2 4 27 1 5 28
- Sean la función de producción Q(K, L) 23 625 (Ki + Ki + 4 Li) , que depende de las cantidades 7. utilizadas de los inputs K y L, y sea el punto (K,L)= (2,4). (a) ¿Cuál es el efecto sobre la producción de un aumento de una unidad en la cantidad utilizada del input L, ceteris paribus? (b) ¿Cuál es el efecto sobre la producción de un aumento de un 1% en la cantidad utilizada del input L, ceteris paribus?Suppose the relationship between your study time and your grade on a History midterm is given by the following table:If you study for Your grade will be4 hours 805 hours 906 hours 93What is the "marginal grade improvement (MGI)" of the 5th hour of studying? What is the "marginal grade improvement (MGI)" of the 6th hour of studying? Why might the MGI be diminishing?The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of labor?
- Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?A car wash firm calculates that its daily production (in numbers of cars washed) depends on the number of n workers it employs according to the formula P=30n-0.05n^2 cars. (a) Calculate the marginal product of labor at employment level of 50 workers. ___ cars/workers. Interpret the results. This means that, at an employment level of 50 workers, the firm’s daily production will increase at a rate of ____ cars per additional worker it hires.MCQ 45 Suppose the production function exhibits constant returns to scale, with diminishing marginal productivities for both capital and labour. For this function, we would expect a fall in employment and an increase in the capital stock to generate: A a fall in the marginal product of labour and a fall in the marginal product of capital I do not want to answer this question. a fall in the marginal product of labour, but the change in the marginal product of capital can't be determined from the information provided D a rise in the marginal product of labour and a fall in the marginal product of capital E a rise in the marginal product of labour and a rise in the marginal product of capital F a fall in the marginal product of labour and a rise in the marginal product of capital