A firm is attempting to maximize output given a budget. Draw a graph that illustrates the output-maximizing input combination. Suppose the cost of capital decreases. Show the new isocost line and the new output-maximizing combination of inputs.
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A: GIVEN The law of diminishing returns states that is
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A: Answer - Thank you for submitting the questions but we are authorized to solve one question at a…
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A: Production function: q = 10L0.5K0.5 ---------- Cost of a unit of labor =20 => w =20 ----------…
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A: Given; Production function; f(L,K)=LK Formula to calculate:- MPK=df(L,K)dKMPL=df(L,K)dLMRTS=MPLMPK
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A firm is attempting to maximize output given a budget. Draw a graph that illustrates the output-maximizing input combination. Suppose the cost of capital decreases. Show the new isocost line and the new output-maximizing combination of inputs.
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- ***There are FOUR parts to the question, all based around the same given data...please answer and explain each and note where graphs are needed*** Given: A farmer raises apples using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor? d. In the long run, the farmer can change both his…24. A specific production process can be represented by the production function, f(x1, x2) = (x 1/2 + x 1/3) 3. A. How much x₁ could the firm give up if it wanted to use 1 extra unit of x2 and still wanted to produce an identical level of output? B. Labeling everything and being precise, draw the isoquant corresponding to q = 4. = 9. C. On the same graph, draw the isoquant corresponding to q D. Between the isoquants you just drew, does the production technology display decreasing, increasing, or constant returns to scale? E. Analytically determine whether the production process has global returns to scale that match your local results from part D. Recall that in order to claim global returns to scale, your result must hold for ALL possible values of x1 and x2.The production function for cups in the image uses a variable amount of labor and a fixed a mount of capital to produce output. The production function exhibits diminishing returns to labor. Suppose the techonology in producingc cups improves. In the graph in the image, show how this will affect the production function.
- For a firm to maximize profit, it must minimize the cost of producing whatever quantity it produces. Use the isocost and isoquant tools to present a firm that is choosing the optimal levels of labor and capital (i.e., tools) to produce a certain quantity and a certain cost. Then, show in your diagram how this firm would respond if it were to expand and spend more on its inputs, assuming it is best for the firm to become more “capital intensive” as it grows. Comment on WHY a firm might best become more capital intensive as it expands, even when the relative prices of labor and capital remain unchanged.Question 4 The firm can use two inputs, L and K. The price of L= 20 and price of K = 30. Total cost = 300. As usual in the two input graph, units of L are on the horizontal axis and K on the vertical. The slope of the isocost line is [Select] The maximum units of K that can be purchased is [Select] The maximum units of L that can be purchased is [Select] 2 pts Is the bundle of K-9 and L- 5 on the isocost line? [Select]Isoquant curves and isocost curves are tools that can explain how a firm might best respond to changes in the production environment. Present an example of an isocost curve where labor and capital are the two inputs, and explain what it is using language someone not trained in economics could understand. Present an example of an isoquant in the same diagram you used for your isocost curve, and draw the isoquant so it cuts the isocost curve twice. Explain what an isoquant is using language someone not trained in economics could understand. Label the two points A and B, where the isocost and isoquant curves intersect. Present a logical argument that explains why the firm should operate neither at point A nor point B, and present a point that would be optimal by drawing a new isoquant curve in the diagram. Add a second isocost curve to your diagram such that the firm is spending more money on inputs. Add a third isoquant to your diagram to show a firm that would become more capital…
- Present a graph of the following. Label your graphs completely1. Using the isoquant map and isocost, show that combination M is the optimum combination of inputs and not combinations E and L.***QUESTION HAS FOUR PARTS - ALL PARTS MUST BE ANSWERED TOGETHER AS THEY ARE DEPENDENT ON EACH OTHER*** 1. A farmer raises apples using land (K) and labor (L), and has an output of ? (?,?) = ? 0.5 ? 0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor? d. In the long run, the farmer can change both his amount of land and his amount of labor. Suppose…A firm uses labor (L) and capital (K) to produce outputs. The following graph shows the iso-quant curves and iso-cost curves facing this firm. The iso-quant curves are the L-shaped curves. Suppose the wage rate of labor is $200 (per day) and the rental rate of capital is $100 (per day). What is the cost of producing 20 units of output (per day) when both labor and capital are variable inputs? Notice that both inputs are variable. alae-2 (3.6) -30 = 20 - 10 O 400 O 600 1000 1200 800
- Suppose a soap-manufacturing production process is described by the following equation: Y = a + b log K + с log L Where, Y= Output (number of soaps produced) K=Capital L=Labor a, b and c are constants Suppose 0<a<1, 0< b<1 a. Find the Marginal Product of Labor (MPL) and Marginal Product of Capital (MPK) in the production of soap b. Is MPL diminishing, increasing or constant as L increases? c. Is MPK diminishing, increasing or constant as K increases?Suppose the price of labor used by a cost-minimizing firm decreases. The firm responds to the price change by changing its demands for certain inputs, but keeps its output constant. What happens to the firm’s use of labor? What happens to the firm’s production costs? Graphically show the new optimal bundle and associated isocost curve on the graph below.Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1 and the cost of a unit of capital is $3. The manager of this firm is interested in finding the following information: a) Type of returns to scale and the marginal products of labor and capital. b) The marginal rate of technical substitution of labor for capital. Graph the isoquant map. c) The firm is currently producing 100 units of output. Find the optimal cost-minimizing quantities of labor and capital. Graphically illustrate this optimal solution using isoquants and isocost lines. What is the minimum total cost? d) The manager now wants to know the K/L ratio to produce anyoutput level at the minimum total cost. Represent graphically the expansion path in the long run.