Q: mathematically derive the slope of isocost line and isoquant and interpret.
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- Consider the fictitious firm, Icelandic Investment Managers (IIM). The company hire investment managers as workers and laptop computers with artificial intelligence (AI) as capital to offer investment advice to clients. Both managers and the AI can provide advice, but they are not perfect substitutes. Draw representative isoquants for the two inputs. What assumptions are you making when you draw the isoquants? If the AI gets smarter, and as a consequence the inputs are more substitutable, what should happen to the shape of the isoquants? Both inputs are costs; managers have to be paid a wage, called “w” and the AI needs electricity, the price of which is “Pe”. This will generate an isocost line for a particular cost level C*. Please draw this, explaining carefully and fully the purpose of the axes. Now we can put these together. For a given output level of advice, A*, show what the optimal level of inputs are for IIM in a diagram. What is the economic interpretation of the intersection…Suppose that during an economic boom labour costs rise by 100% and are expected to stay at that level for a long time, while the rental cost of capital stays the same. Draw the firm’s output expansion path before and after the boom. Assume that the firm has downward sloping strictly convex isoquants. (Draw several isoquants and isocosts). Put labour on the horizontal axis.Suppose that during an economic boom labour costs rise by 100% and are expected to stay at that level for a long time, while the rental cost of capital stays the same. Draw the firm’s output expansion path before and after the boom. Assume that the firm has downward sloping strictly convex isoquants. (Draw several isoquants and isocosts). Put labour on the horizontal axis. New isocosts will have slope equal to [4 times, 3 three, twice, exactly, one half, one third, one fourth] the slope of the original isocosts. The firm will hire [more, less, the same amount of ] labour and [more, less, the same amount of] capital to produce the same amount of output. Output expansion path will [shift/ tilt to the right, shift/tile to the left, stay the same] .
- Draw two isoquants for this firm. On the same graph, draw and label firm α’s expansion path at these prices of capital and labor.In production theory, diminishing rate of technical substitution(RTS) shows how one input is substituted for the other. This also means that isoquants must be convex . True or false and explain2 true or false The closer an isoquant is to a straight line, the closer the inputs are to being perfect complements
- 1- Define the following Terms - Isoquant - Marginal rate of technical substitution - Production function - Economies of scopeQ2. Define marginal physical product of labor (MPP) and marginal cost of product (MC). How are these two related? Why is MC called the mirror image of MPP? Explain.If a firm experiences diminishing productivity of labor, the marginal product Question 31Select one: a. increases as total product decreases. b. decreases as total product increases. c. decreases as total product decreases. d. increases as total product increases.
- Figure 6.4 above shows the isoquants for the production of steel. In which regions of production are there increasing, decreasing, and constant returns to scale?Example about isoquants and isocost curveThe following table gives the output achievable for various combinations of inputs. There are only two inputs used in production, labour and capital. labor input capital input 1 2 3 4 5 1 20 40 55 60 65 2 40 50 65 70 75 3 55 65 75 80 85 4 60 70 80 90 95 5 65 75 85 95 100 Explain the meaning of an isoquant . Draw the isoquants for the output level of 65 and 75 on the same graph.Define and explain the returns to scale for production with those inputs given above table.
