he set of feasible netputs is Y = {(₁, ₂) € R²: 11 ≤0, and 2₂ ≤ √√-₁}. As a function of p > 0, give the y* (p) that solves the problem max,ey P.y. -. Interpret your results using the marginal productivity of the input and the relative prices of inputs and outputs. . Partially check your answer by verifying that the Law of Supply and De- mand holds.
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- 4:34 D *3 all 100% I 2. 3 When the inputs price ratio (slope of cost line) is greater than the MRTS, (MPK/PK > MPL/PL) the producer should use .. to minimize the cost. A More labar C Mare labor and more capital B More Capital D| None of the above 4 The optimal production method A maximizes output regardiess of cost C minimizes the normal rate of return B| maximizes inputs. Dminimizes cost 5. Refer to the information provided in the following figure, If this firm's cost of labor is $10 per unit, and the isocost line represents a total cost 2000. How much is the cost of capital per unit? 100 q-300 -200 -100 200 Units of labor Linits of capital2. Is it possible to avoid Diminishing Marginal Return? Why? Explain comprehensively.If the slope of the total productivity line is decreasing as output increases, what does that say about marginal productivity? Selected answer will be automatically saved. For keyboard navigation, press up/down arrow keys to select an answer. a b Question 32 C Marginal productivity is increasing. Marginal productivity is decreasing. Marginal productivity is flat (constant). d Cannot be determined from the information given.
- In terms of dynamic programming, explain the optimality principle. .1. Consider the production functions for good X and good Y: X = K? +L ; Y= 20VKL A. Show and discuss which production function(s) exhibit(s) diminishing marginal productivity of labor and capital. B. Show and discuss which production function(s) exhibit(s) diminishing MRTSLK. C. Suppose capital and labor are doubled, solve for the returns to scale of each production function, and interpret your results.Digging calms by hand in Sunset Bay requires only labor input. The total number of calms obtained per hour (q) is given by :Q = 100√LWhere L is labor input per hour. A. Graph the relationship between q an LB. What the average productivity of labor in Sunset Bay? Graph this relationship and show that output per unit of labor input diminishes for increase in labor input. C. It can be shown that the marginal productivity of labor in Sunset By is given by:MPL =50√LGraph this relationship and show that labor’s marginal productivity is less than average productivity for all values of L . Explain why this is do.D. Explain the concept of diminishing returns to labor and how this concept related to increasing marginal costs.
- 13. Suppose you have a production technology given by f(x1, x2) = min{2x₁, x2} and you are producing at the point where x₁ = 10 and x₂ = 20. (a) Explain in words what we mean (generally) by the ‘marginal product' of an input in production. (b) For the production technology in this question and the initial point x₁ = 10 and x2 = 20, what is the marginal product of a small increase in input 1? (c) Suppose input 2 increases and you are now at the initial point x₁ = 10 and x2 = 30. Relative to your answer in part (b), does the marginal product of input 1 decrease, increase, or stay constant? Explain briefly.What is the difference between economies of scale andeconomies of scope? How do firms consider these wheninvesting in processes?(04.Suppose we are given (he constant returns to scale (CES) production function q= { ßa + aa }1/a a. Show that the marginal product of Beta is (g/B) and marginal product of Alpha (q/a)** b. Show that RTS = (2/B); I lence or otherwise shov that the ò =-1/(1-a) 1-a
- When thinking about cost analysis in Microeconomics, what are the real-world problems that occur when applying theories of scale? Describe and give an example of each.Donot forgett to make stages of production graphically..Consider a company using the economic production quantity model. a. Derive the percent change of total cost if the lot size is different than the optimal by a factor of (1+z). b. How would the total cost change if the holding cost in the model is reduced 30 percent? c. Derive the percent cost difference if decide to increase production rate by a factor of (1+w)