An economy has 8 units of labor and 8 units of capital that are allocated between industry X, with the DRTS production function x = K^(1/4)L^(1/4), and industry Y, with the CRTS production function y = K^(1/2)L^(1/2). Derive and graph the Production Possibilities Frontier for this economy. All consumers believe X and Y are perfect complements with tastes U = min (Y, 2X). Calculate production levels that are consistent with tastes and show these in your diagram.
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An economy has 8 units of labor and 8 units of capital that are allocated between industry X, with the DRTS
production function x = K^(1/4)L^(1/4), and industry Y, with the CRTS production function y = K^(1/2)L^(1/2). Derive and graph the Production Possibilities Frontier for this economy. All consumers believe X and Y are perfect complements with tastes U = min (Y, 2X). Calculate production levels that are consistent with tastes and show these in your diagram.
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- 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?Suppose two economies Home (H) and Foreign (F) produce two goods, bread and wine, with only one production factor: labour. Production technology, expressed as marginal product of labour (MPL), is given in the following table: Technologies expressed as MPL Bread Wine Home 1/6 1/12 Foreign 1/4 1/2 Suppose that Home has 2400 units of labour and Foreign has 1800 units of labour. a. ) Derive the Production Possibilities Frontier (PPF) and the Consumption Possibility Frontier (CPF) for Home and Foreign, with bread on the horizontal axis and wine on the vertical axis. What is the autarky equilibrium price of bred relative to wine in each country? b.) What country has the absolute advantage in producing each good? What country has the comparative advantage in producing each good? Briefly explain the difference between these two concepts. Suppose both countries are now free to trade. The world relative price of bread is 1. c. What is the pattern of specialisation and trade?…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 units of X and Y will be produced?
- 5. Suppose food (F) and clothing (C) are produced using only labor. The production functions are given by: F = (LF)0.5 C = 0.5(Lc)0.5 Where LF is labor devoted to food production and Lc is labor devoted to clothing production. Labor supply is fixed at 100. Suppose society's preferences can be represented by: U(F,C) = (FC)0.5 Solve for the equilibrium outputs of food and clothing and for the relative price of food (PF/ Pc). LF + Lc = 100Supermarché Jean Claude has decided to manufacture its own brand of non-alcoholic beverages, called NAB, and chocolate bars, called S-JC. A certain amount of money has been allocated to the production of these two products. Jean Claude believes in the old saying that a picture is worth a thousand words, and once again, he has called on you. This time, he wants to see diagrams that illustrate the effects of each of the following events on the production possibilities for NABS and S-JCs so he can visualize the situation. (a) A new and more efficient method of producing non-alcoholic beverages is discovered. (b) The demand for both non-alcoholic beverages and chocolate bars increases. (c) More workers are hired to produce S-JCs. (d) Resources are transferred from S-JC production to NAB production. (e) All workers are trained so that the quality of their labour services improves. Instructions Produce the series of graphs with accompanying texts (150-175 words) so that Uncle Jean Claude…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…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 .An economy depends on two commodities, bees and honey. It takes 3/4 units of bees to produce 1 unit of honey and 1/2 unit of honey to produce 1 unit of bees. Find the production required to satisfy a demand of 100 units of bees and 300 units of honey. Hint: x = (I - A) ^ - 1 * D Please step by step answer.
- How does a consumer’s optimal choice of goods change if all prices and the consumer’s income double? (Hint: focus on the budget constraint. You don’t have to, but you can use an example to support your answer).5. Output is produced according to a production process given by: Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then what is the cost-minimizing combination of K and L capable of producing 32 units of output?Consider an economy that produces two goods , X and Y. Use a production box diagram to construct the production possibility frontier for these two goods. Also indicate the optimal consumption point and price ratio that will prevail. Suppose now that technical progress causes the X isoquants to shift towards the origin. How will this affect the production possibility frontier, the optimal consumption point and equilibrium price ratio for X and YThe 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