Suppose the economy of Utopia has a labor force of 600 workers, 100 units of capital and 400 hectares of land. It produces manufactured goods (M) which use labor (LM) and capital (K) in production and agricultural goods (A) which use labor (LA) and land (T) in production. The production functions are given by:
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- Assume an economy producing only two goods (shoes and computers) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum. Production in this economy is subjected to the law of diminishing marginal returns and resources are assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers and vice versa is 1. On the basis of the foregoing assumptions, answer the following questions: i. Draw the economy’s production possibility frontier on hindsight of the relevant assumption. What happens to the PPF when technological change overwhelmingly favours the production of computers? What happens to the PPF when the economy discovers an improved technology for producing shoes? Assume now that the sacrifice ratio is greater than 1, show what will happen to the shape of the production possibility frontier. vii. Mention three (3) conditions under which the sacrifice ratio between the goods will be…Ab 11 Economics A production function is given by the equation Q = 48L^0.5*K^0.5. Where L is the number of labor units and K is the capital units. Find the marginal product of labor (QL) and the marginal product of capital (Qk) at L=9 and K=16.Consider a specific-factors model where two Countries, Denmark and Tanzania, use labor to produce cake (C) and helicopters (H). However, arable land (A) are a factor specific to cake, and jerrycans (J) are a factor specific to helicopters. Suppose that Tanzania has L = 100 workers, J = 40 jerrycans, and A = 1000 arable land. The production functions and marginal products of labor for cake and helicopters are: C = 4 x Lc0.5 x A0.5 MPLc = 2 x Lc-0.5 x A0.5 H = 4 x LH0.5 x J0.5 MPLH = 2 x LH-0.5 x J0.5 In Tanzania, the price of crystals is 20 and the price of hyperdrives is 200. In this case, the wage rate will be ________ and ________ workers will be employed in the cake industry and __________ workers will be employed in the helicopter industry.
- An economy depends on two basic products, wheat and oil. To produce 1 metric ton of wheat requires 0.25 metric tons of wheat and 0.33 metric tons of oil. Production of 1 metric ton of oil consumes 0.08 metric tons of wheat and 0.11 metric tons of oil. Find the production that will satisfy a demand for 540 metric tons of wheat and 870 metric tons of oil. The input-output matrix is A= 0.25 0.08 0.33 0.11 .In 2000, the country of Cobra Island has an initial level of capital set at 10 units. The population of Cobra Island is unknown, but we do know that it grows each year at some constant rate. The level of total income is 500 cobra dollars. Finally, the total production function of Cobra Island can be described as Y=10*L1/2k1/2 a)What is the initial population of Cobra Island? b)Let the wage of labor is 0.4, and the rental rate of capital is 0.6. The capital to labor ratio after two years (in 2002) is 50 while the amount of workers is 1000. The growth rate of capital is 6,970%. The growth rate of labor is 100%. Find the GDP of Cobra Island. c)How much labor is there in Cobra Island one year after the initial year (or in 2001)? d)The growth rate of income is 1,089%. Find the Solow Residual. Do not give the answer as a percentageSuppose China can produce two goods, cloth and food and has three factors of production labor (L), capital (K) and Land (T for terrain). Food is produced using land and labor while cloth is produced using capital and labor, hence, labor is a mobile factor. Keeping in mind the Specific Factors Model, answer the following questions a) What are the production functions for cloth and food? b) Write down the wage equations for each sector and the slope of the production possibility frontier. c) Drive the production possibility frontier for China [hint 4 quarter diagram]
- Consider the production function Y = z * K^1/3 * N^1/3 * L^1/3 where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land. Question text If we double the technology factor, z, then output will double. Question 17Select one: True False Question text If we increase the population, and therefore the workforce, then if nothing else changes, the average product of labour must increase. Question 18Select one: True False Question text We would need to increase capital input by a factor of 8 to double output. Question 19Select one: True False Question text Increasing technology will increase labour productivity. Question 20Select one: True FalseThe information on three different technologies named as q, v and x is listed in the table below. Note that all of these technologies use different combinations of two types of factors of production, labor and capital, to produce 1000 units of output. Consider the first scenario where the per unit prices of the inputs, labor and capital are $50 and $25 respectively. Technology No of Labors Capital (tons) Cost value ($) A 10 50 B 30 20 C 50 10 Now imagine that a discovery has been made which has led to labor advancements leading to a reduction in per unit price of labor to $10, ceteris paribus. Which technology will a typical firm adopt under these changed circumstances and why? Using the value of costs found, what is the value of the economic rent for this firm?Suppose that a natural disaster destroyed a significant amount of farmland in the Midwest. Provide examples of how this flooding affects the marginal productivity and price of inputs of the remaining land, labor, and capital.
- There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A’s marginal rate of technical substitution of labour for capital is 4 while B’s marginal rate of technical substitution of labour for capital is 2. A. Is the current production of the two firms efficient? If not, describe an exchange of inputs that would improve efficiency. B. Can these production levels of the two firms be observed in a perfectly competitive equilibrium of a production and exchange economy? Explain.Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels:(Photo)Assuming that the price of labor (PL) is RO 2 and the price of capital (PK) is RO 3, calculate the total cost of production for each of the five levels of output using the optimal (least cost) technology at each level. How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? (Graph the total cost of production as a function of output. (put cost on the Y-axis). Which technology is the cheapest at all levels of output. Select one:a. None of the other three answersb. Technology Bc. Neither A Nor Bd. Technology AThe productive capability of an economy is such that to produce 5 units of military good it takes 2 workers to be employed while 10 units of consumer goods require 3 workers. Resources are limited in such a way that only 75 units of military good can be produced when all resources are employed. a) Construct the production possibility schedule and curve for this economy. b) Graphically represent what would happen if 12 additional workers were added to the economy. c) Graphically represent what would happen if the productivity of the workers were reduced to 2 units of military good and 5 units of consumer goods. d) Graphically represent what would happen if productivity for military goods remained the same but it now required 2 workers to produce 10 units of consumer goods