2. Suppose that computers use 2 units of capital for each worker, so that Kc = 2. Lc, whereas shoes use 0.5 unit of capital for each worker, so that Ks = 0.5 Ls. There are 100 workers and 100 units of capital in the economy. b) a) Solve for the amount of labor and capital in each industry and graph them in a box diagram. Suppose that the number of workers increases to 125 due to immigration, keeping total capital fixed at 100. Again, solve for the amount of labor and capital used in each industry and show in your previous graph. c) Suppose instead that the amount of capital increases to 125 due to FDI, keeping the total number of workers fixed at 100. Again, solve for the amount of labor and capital used in each industry. Graph in a new box diagram
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- Suppose that production function of certain devices is determined by: q = k * L - 0.8 k2 - 0.2 L2 Where q represents annual quantity of devices produced, k represents annual quantity of capital factor, and L represents annual quantity of labor factor. (a) Suppose k = 10; draw a graph with average and total labor productivity. What is level of labor (L) factor at which average productivity reaches a maximum? How many devices are produced at that point? (b) Assuming again that k = 10, plot Marginal Product (MP) curve. At what level do we have that labor (L) factor is MP = 0? (c) Suppose capital (k) factor were to increase to k = 20. How would your previous answers change?Question 15 Consider the following figure (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a level of K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; five units of labor is shown as reference in the horizontal axis; the corresponding production for this level of labor is 200; the graphs slope is initially increasing, then there is an inflexion point to the left of five levels of labor; after this inflexion point, the slope of the graph is decreasing; a line that passes through zero and is tangent to the graph is also shown; this line is tangent to the graph for a level of labor that is to the left of 5.) Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). From the…The concept of diminishing returns to a factor of production applies not only to capital but to labor as well. Prior to the Industrial Revolution, there was no sustained growth in living standards. Draw a graph to illustrate the relationship between population and output produced, where population is measured on the horizontal axis, both pre- and post-Industrial Revolution. 1.) Using the 3-point curve drawing tool, draw the production curve showing diminishing returns to labor. Label your curve 'Pre.' 2.) Using the 3-point curve drawing tool, draw the production curve after the Industrial Revolution. Label your curve 'Post. Carefully follow the instructions above and only draw the required objects. a
- Short Answer 12) Using the following table, which of the production choices (a, b, c, d, e) are technologically efficient? If the price of capital is the same as the price of labor, which choice is economically efficient? Finally, explain the relationship between technological efficiency, economic efficiency, isoquants, and isocost lines. Feel free to use a graph to help show what you are explaining if you'd like, but make sure to clearly label everything on your graph so I can see what you are describing in the graph. Production Technique Output 100 Capital Labor 15 B 100 6. 16 C 100 12 9. 100 12 417. For a certain good the production function is given by the equation q = q²qc, where q is the produced output in units of 1000 and qL and qc are the number of units of labour and of capital invested in the production process. Assume that one unit of labour costs 10 units of money and one unit of capital costs 5 units of money. (a) Show on a graph which combinations (qL, qc) generate exactly 64 000 units of output. Put qL on the horizontal axis of the graph and qc on the vertical axis. (b) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce 64 000 units using a budget of exactly 100 units of money. (c) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce 64 000 units in the cheapest possible way.Table 3-7Assume that the farmer and the rancher can switch between producing meat and producing potatoes at a constant rate. Labor Hours Needed to Make 1 Pound of Pounds Produced in 24 Hours Meat Potatoes Meat Potatoes Farmer 6 4 4 6 Rancher 3 8 8 3 Refer to Table 3-7. Assume that the farmer and the rancher each has 24 labor hours available. If each person divides his time equally between the production of meat and potatoes, then total production is Group of answer choices 6 pounds of meat and 4.5 pounds of potatoes. 5.5 pounds of meat and 8 pounds of potatoes. 12 pounds of meat and 9 pounds of potatoes. 5 pounds of meat and 5.5 pounds of potatoes.
- 5 Supposing that a single consumer works for a firm, the quantity of labor input for the firm, N, is identical to the quantity of hours worked by the consumer, h - l. Graph the relationship between output produced, Y on the vertical axis and leisure hours of the consumer, l, on the horizontal axis, which is implied by the production function of the firm. (In Chapter 5, we refer to this relationship as the production possibilities frontier.) What is the slope of the curve you have graphed? PLEASE DO NOT COPY OTHER PEOPLE'S WORK AND GRAPHQuantities Produced 225 220 215 210 205 200 195 190 185 180 175 170 165 160 155 150 145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 0 1 2 3 Number of Workers units of output. productivity. The graph above shows the relationship between the daily quantities of a good produced by a small firm and the number of workers hired, given all the other resources available to the firm. For example, one worker can produce 30 units and two workers can produce 55 units. Such a relationship between a production factor (here labor) and the amount of output produced is called a production function. Currently the nominal wage rate is W = $200 per worker per day and the price of the product is P = $10 per unit. Of the amount of increase in production noted above, 4 Now suppose that the firm installs some new machines and offers the workers some rigorous training and as a result the productivity of the workers increases. In particular, the marginal product of each worker…Consider the following production diagram: 12 10 A Capital 6 2 0 0 1 Labor 4 For each of the five labeled points (A, B, C, D, and E), determine whether the correct levels of labor and capital are being used. If the correct level is not being used, explain why, and what change should be made. Hint: Start by identifying the optimal point. Being able to compare to the optimal point will assist you in determining the changes that need to be made.
- 2) The production function of a factory has the following characteristics: • Use workers (x1) and machines (x2). • It is not capable of producing if it does not contract one of the two factors of production, even if you hire the other. • You can increase production a given percentage, hiring the percentage more workers without hiring more machines. • When you hire 1 worker and 1 machine, you can produce 8 per day. Which of the following production functions are consistent with the above and why? 1/21/2 a. y = 8x;'"x2" b. y = xx2 %3D 8 c. y = min{8x1,8x2} d. y = min{x, x} %3DASAPYou run a factory that uses pottery wheels to make pots. You can hire anywhere between 1 and 3 skilled artisans (workers), and you can rent 1 or 2 pottery wheels (machines). Pots sell for $125 each. The total product of your factory is shown in the following table. Number of Machines (Capital, K) 1 Pottery wheels are 2 1 8 10 Number of Workers (Labor, L) 2 11 14 3 13 17 Suppose you rent one machine and hire one worker. You would be willing to pay $ to hire a 2nd worker. (Consider the value of the marginal product of labor.) Suppose you rent one machine and hire one worker. You would be willing to pay a rental rate of up to $ Suppose the wage is $350. If you have one pottery wheel, the number of workers you would want to hire is to acquire a 2nd machine. (Consider the value of the marginal product of capital.)