Consider an economy with an endowment of L = 60 units of labor. The production functions are X = 4Lx and Y = 1.5Ly, where X and Y are consumption goods and Lx and Ly indicate how labor is allocated. If the total labor endowment is equally divided towards producing goods X and Y, then the resulting out is (X, Y) =
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Consider an economy with an endowment of L = 60 units of labor. The production functions are X = 4Lx and Y = 1.5Ly, where X and Y are consumption goods and Lx and Ly indicate how labor is allocated. If the total labor endowment is equally divided towards producing goods X and Y, then the resulting out is (X, Y) =
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- For the Cobb-Douglas production function P and isocost line (budget constraint, in dollars), find the amounts of labor L and capital K that maximize production, and also find the maximum production. Then evaluate and give an interpretation for |å| and use it to answer the question. (a) Maximize P = 2000L3/5K2/5 with budget constraint 15L + 32OK = 8000. L = K = P = (b) Evaluate and give an interpretation for |21. Each additional dollar of budget increases production by this amount. (c) Approximate the increase in production if the budget is increased by $80. unitsa) What are the determinants of production? Explain.b) Suppose that an economy’s production function is in the Cobb–Douglas form with parameter α = 0.3. What is the production function equation? What does each component stand for?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 .
- A country's production is described by the function 2 1 f(x, y) = 30x³y3 units, when x units of labor and y units of capital were used. a) Compute and f,- b) What is the marginal productivity of labor and the marginal productivity of capital when the amounts expended on labor and capital are 100 units and 30 units, respectively? c) In order to increase the country's productivity, should the government have encouraged capital investment rather than increasing expenditure on labor?A firm’s production function is - y = f(X1, X2)= X11/2 + X1X2 , Where X1≥0, X2≥0 1. Write down the firm’s production possibility set, and its input requirement set. 2. Is this production function concave, quasi-concave? 3. Is this production function homogenous? 4. Find its returns to scale when X1=1, and X2=1Let y = f(x1, x2)=x11/2 + x1x2 be a firm’s production function, where x1≥0, x2≥0. Write down the firm’s production possibility set, and its input requirement set. Is this production function concave, quasi-concave? Is this production function homogenous? Find its returns to scale when x1=1, and x2=1.
- Suppose the economy has 100 units of labor (L) and 100 units of capital (K), and it chooses to allocate three times more labor and capital in the production of good X than in good Y. Suppose also that the production of goods X and Y are represented by the following functions: X = LX0.25KX0.25; Y = 2LY0.25KY0.25. Compute for Lx, Ly, Kx and Ky Calculate the MRTSLK of each firm Is this allocation efficient? How so? How many unit of X and Y will be produced? Suppose the utility function of the two individuals in the economy is given by UA = 2XA0.5YA0.5 ; UB = XB0.5YB0.5 and X and Y are allocated equally between the two individuals. Compute for XA, YA ,XB ,YB Calculate the MRSXY of each individual Is the allocation efficient? How so? Determine if at the current allocation, the efficiency in optimal mix attained. Compute for MRTXY What is the MRSXY? Is optimal mix efficiency attained? How so?Consider the following production function: Q = 100L0.5K0.5 subject to the budget constraint 5L + 10K = 75; where L is labour and K is capital. Derive the capital to labour ratio.Answer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.
- Elsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = BW where B is the amount of bananas she consumes and W the amount of water. Her production function for bananas is B = 6LB where LB is the amount of labour time she devotes to bananas. Her production function for water is W = 2LW where LW is the amount of labour time she devotes to water. If the total time she has available is 10, what should she do to maximize her utility?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. Why are points outside the frontier unattainable? iii. Identify three ways by which the economy can attain the level of production outside the PPF. 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…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…