6. Consider the following Cobb - Douglas utility function: U = χαγβην *Note, it should be assumed that a, B.y > 0 Show that this production function can exhibit increasing returns to scale globally while maintaining diminishing returns for each individual input.
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- I badly need help. What is the intuition behind the assumption that production functions are characterized by diminishing marginal returns? Discuss and illustrate.1. Given the following production function Q = 20L2K and the unit prices of labor and capital to be Birr 48 and 12 respectively, then a. What combination of labor and capital maximizes output with a cost of Birr 720? b. What is the maximum output? c. Show the output maximizing condition graphically.Answer the given question with a proper explanation and step-by-step solution. Ned’s Tuna has the following production function: q = K3/4L1/4, Where q is the number of tunas per hour, L is the number of workers and K is the number of boats. Suppose that w = $20/hour (PL) and r = $30/hour (PK). a. Find Ned’s marginal product of labor (MPL). Does it exhibit diminishing marginal returns? b. Find Ned’s marginal product of capital (MPK). Does it exhibit diminishing marginal returns? c. Find and draw an isocost function for C
- Does the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?In the short run, a firm cannot vary its capital, K=2, but it can vary its labor, L. It produces output, q. You are given two production functions. (a) q = 10L + K MPL = 10 (b) q = L0.5K0.5 For each production function, please determine whether the production function will show diminishing marginal product (diminishing marginal returns) as labor increases. You must give an explanation for each answer. (Note: Diminishing returns of labor refer to the decrease in marginal product of labor as the quantity of labor increases).Homework Study Question 4 - Long Answer Please help me with PART B I understand part A and have already answered it, but part b im not getting! Our closed economy has a production function Y = A•F(K,LxE), where Y, K, L, E & A all have their usual meanings as per our lectures & course textbook. Also, this production function exhibits all the usual mathematical/economic properties we usually assume: positive marginal products, diminishing marginal products, complementarity between K & (LxE), and constant returns to scale. The aggregate consumption function depends negatively on the real interest rate, the government budget is balanced initially & the economy is in both a long-run equilibrium and steady state initially. The population growth rate is 2% per year, capital depreciates at a rate of 3% per year, the saving rate is 25% and technology is constant. Suppose the level of labour effectiveness (E) suddenly permanently rises by 10%. Use the long-run classical model…
- Q.2 Considering short-run production with fixed capital input and variable labor input, explain the relationship between Marginal Product and Marginal Cost. Can you give any reason why indifference curves are convex to the origin or bowed inward? (Hint: You can attempt this question without the use of graphs)Discuss the impact of rational self-interest on each of the following decisions. Whether to attend college full time or enter the workforce full time Whether to buy a new textbook or a used one Whether to attend a local college or an out-of-town college (Production in the Short Run) Complete the following table. At what point does diminishing marginal returns set in? Units of the Variable Resource Total Product Marginal Product 0 0 — 1 10 — 2 22 — 3 — 9 4 — 4…1. The production function for the personal computers of DISK, Inc., is given by q = 10K0.5L0.5,where q is the number of computers produced per day, K is hours of machine time, and L ishours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function q = 10K0.6L0.4. a. If both companies use the same amounts of capital and labor, which will generatemore output?b. Assume that capital is limited to 9 machine hours, but labor is unlimited in supply. Inwhich company is the marginal product of labor greater? Explain.
- Suppose a firm’s production function is ? = ?2?. a) Determine the labor and capital demand functions. b) Are capital and labor normal or inferior inputs in this production process?Give only typing answer with explanation and conclusion Consider a production function with two inputs: f(x1,x2) = (x1)a(x2)b Suppose that a = 0.7 and b = 0.7. What type of returns to scale does this production function exhibit? Type 1 for increasing, 0 for constant, and -1 for decreasing.Assume that Donnell Corp. is currently producing 500 units of output per period, using 25 units of labor and 20 units of capital. Values for the marginal product of each input and the prices of the inputs are as follows: MPK = 100, MPL = 200, w = 2, and r = 3. Given the information above, which of the following is true? a. The firm is currently using the optimal levels of capital and labor. b. The firm should increase labor and reduce capital usage. c. The firm is not using the optimal levels of capital and labor, and it is impossible to determine the optimal levels from the given information.