d) If the quantity of labor supplied increases by 1%, what is the increase in the firm's output? State your answer in terms of expenditure shares. e) If the quantity of labor supplied increases by 1%, what is the change in the real wages of workers? f) If this production function is to represent the US economy, what is a reasonable value to choose for a? Why?
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- The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1Exercise 11 Question Help Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5KO.5/L0.5 - 0.5g/L 70- and MPK = 5L0.5/K.5 - 0.5g/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- -q= 280 q= 140 98 Suppose now that the firm wants to increase output to 280 units. If capital is fixed 0- in the short run, how much labor will the firm require? 70 84 L, Units of labor 14 28 42 56 112 The firm will now require units of labor. (Enter your response rounded to two decimal places.) K, Units of capital2. The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3K1/3, where P is the number of anvils produced when L is the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. c. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. Only need paVAS e and fl
- 4. Show that the law of diminishing marginal productivity holds for the production function Q=6L² - 0.2L'3. a. b. C. d. Don Corneo's firm has a Cobb-Douglas production function given as: Y = AK 0.5 N 0.5 Show that the production function exhibits Diminishing returns with respect to Capital, K. Show that the production function can exhibit Constant returns to scale Estimate the output per worker, N. Calculate the elasticity of substitution, o.1. Let y = f(x1, x2)=x11/2+ X1X2 be a firm's production function, where x20, x220. - a. Write down the firm's production possibility set, and its input requirement set.“ b. Is this production function concave, quasi-concave? c. Is this production function homogenous, homothetic? + d. Find its returns to scale when x1=1, and x2=1.e
- IV. Will can produce a higher grade, Gw, on an upcoming economic exam by studying. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, Gw = 2.5A0.36R 0.64. His roommate David's grade production function is G) = 2.5A0.25R0.75 a. What is Will's marginal productivity from studying supply and demand problems? What is David's? b. What is Will's marginal rate of technical substitution between studying the two types of problems? What is David's?1. A firm can manufacture a product according to the production function Q = F(K,L) = K³/4L¹/4 a. Calculate the average product of labour, when the level of capital is fixed at 16 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 81 units of labour? b. Find an expression for the marginal product of labour when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labour depends on the amount of labour hired by calculating the marginal product of labour for 16 and 81 units of labour. c. Suppose capital is fixed at 16 units. If the firm can sell its output at a price of £100 per unit and can hire labour at £25 per unit, how many units of labour should the firm hire to maximise profits?X 15:01 EC5011 - Seminar 2.do... II. Problems and Exercises .ıl 4 1. Consider the following production function: . Does this production function exhibit constant returns to scale? (Hint: Replace K and L by 2K and 2L, respectively, and check if F(2K, 2L) = 2F(K, L).) 2. Consider the following production function: . a. Calculate the marginal product of labour. b. Calculate the marginal product of capital. c. Does this production function exhibit diminish MPL and MPK? d. Does this function exhibit constant returns to scale? 3. Suppose represents the production function of both Mexico and Spain. Use the following information to answer the next questions. L = Population K = Capital Y = Output Country (millions) (trillion) (trillion) Mexico 105 0.18 1.0 Spain 45 0.74 1.7 a. Calculate total factor productivity for both countries using the PF in question 2. b. Calculate per capita income for both countries. c. Explain the difference in per capita income. 4. A snack food factory in the Tuas…
- Question 8 of 13 The following diagram depicts the production function of the farmers, where diminishing average product of labour is assumed. At A the average product of labour is 500,000/800 = 625 kg of grain per farmer. At B the average product of labour is 732,000/1,600 = 458 kg of grain per farmer. If you know that for 2,800 farmers the grain output is 894,000kg, then which of the following is/are correct? Kilogrammes of grain produced (thousands) 900 800- 700- 600- 500 400- 300- 200- 100- 0 0 400 800 B 1,200 1,600 Number of farmers 2,000 2,400 2,800 OA. The average product of labour when the labour input is 2,800 is 300. OB. The decreasing slopes of the rays from the origin to the production function along the curve indicate the decreasing average product of labour. OC. If the production function curve is an upward-sloping straight line, then there is no diminishing average product of labour. OD. It is possible that initially there is an economy of scale: for example, going from…Question 8 m Consider the following (Cobb-Douglas) production function: f(x1, x2) = Ax1α1 x2α2 , where A, α1, α2 > 0. The marginal product of input 1 is: a. Positive b. Zero c. Not enough information d. Negative Full explain this question and text typing work only thanksProblem 10 Tony's Little Italia restaurant produces pizza. The production of pizza requires only cheese and dough, with the production function set as f(c,d) = c05d0.5. Suppose that a pizza sells for £6, the price of cheese is w, and the price of dough is wd. Which of the following equations states that the value of the marginal product of cheese is equal to its price? a) 3c-0.5d-0.5= wd*Wc b) 6c05d0.5 = Wc c) 0.5c-0.5d0.5 = Wc d) 3c-0.50.5=Wc