a. Demonstrate that the production functions satisfy the conditions for monotonically increasing, diminishing return to labor, and constant returns to scale. b. If labor markets are perfectly competitive, in each sector the value of the marginal product of labor will be equal to the wage rate. Write these two conditions. Make sure to base your answer on the provided production functions. c. Combine the two conditions above to get the relationship between the relative price of corn and potatoes, and the allocation of labor to the two sectors (Lc, LP). If the relative price of corn decreases, what happens to the allocation of labor between the two sectors?
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- 11 11. Consider the following economy: There are three goods, legume, tillip and quillip, two consumers (called 1 and 2), and two firms (called x and y). Firm x is owned entirely by consumer 1 and makes tillip out of legume according to the simple linear production technology t :::; 3l . That is, for every unit of legume input, this firm produces three times as many (or less) units of tillip. Firm y is owned entirely by consumer 2 and makes quillip out of legume according to the production technology q = 4l. Each consumer initially owns 5 units of legume. Consumer 1 has utility function u1(t, q) = 6 + .4ln(t) + .6ln(q). Consumer 2 has utility function ui(t, q) = 8 +ln(t) + ln(q). (a) What is the general equilibrium of this economy? Assume that firms take prices as given and are profit maximizers, and consumers take prices as given. When you give prices, normalize…The data below describe the current production possibilities for an economy that produces two goods: Livestock Products and Aquaculture products Quantities that can be produced per month with the currently available resources Aquaculture products 6000 5900 5700 5400 5200 4100 Livestock products 0 100 200 300 350 500 Label point A B C D E F Required: (a) Explain the existence of opportunity costs in this situation. (b) Plot the PPF. Put Livestock goods on the vertical axis; Aquaculture on the horizontal axis. Label the points. Be sure each axis is to scale. Scales can differ between axes. (c) “Your PPF slopes down because of tradeoffs.” Explain that sentence in words that make sense to someone not taking economics.The budget constraint model and the production possibilities frontier (PPF) model both illustrate (select ALL that apply): O allocative efficiency O productive effieciency O a curved line to represent both the budget constraint and the PPF the tradeoffs in choosing more of one good at the cost of less of the other O comparative advantage O constraints on what we can have due to scarce resources
- Hi can you please help with following questions I am not sure how to solve them please assist with question A You are the sole survivor of a shipwreck on a desert island. You do not expect to be rescued.You can either use your time to grow food to consume immediately, or to build new tools andbuildings (capital) which will increase your supply of food in future years. a) Sketch your initial production function (total output of food + capital in terms of yourlabour input), and show how to turn this into a feasible set. Show your optimal choiceof how you spend your time, assuming you initially consume everything you produce.The table below presents production schedule of apples and bananas in the country of mistania - assume that these are the only two goods that Mistania produces. Each row represents a specific set of apples and bananas that Mistania could produce. Suppose Mistania was currently at Senario C, producing 10 bananas and 80 apples. According to the data in this table, if Mistania wanted to produc 1 more banana, how many fewer apples will it need to produce? Scenario Bananas Apples A 0 100 B 5 90 C 10 80 D 15 70 E 20 60Specify and explain the typical shapes of marginal-benefifit and marginal-cost curves. How are these curves used to determine the optimal allocation of resources to a particular product? If current output is such that marginal cost exceeds marginal benefifit, should more or fewer resources be allocated to this product? Explain.
- Figure 1 The production possibility frontier ABCDE is a production possibility frontier. It shows the different combinations of goods which can be produced if all resources are fully and efficiently utilised. The economy can produce at any point on the line. It cannot produce at G because the PPF shows the maximum that can be produced. It can produce within the PPF,05 such as at F, but less will be produced than the maximum possible. Non-manufactured goods 50 40 30 20 10 0 A 10 B Ti C 20 30 Manufactured goods G D E 40Suppose 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? Briefly…Assume an economy producing only two goods (shoes and computers) with a fixed amount ofproductive 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 resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice 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 relevantassumption.ii. Why are points outside the frontier unattainable? iii. Identify three ways by which the economy can attain the level of production outside thePPF. iv. What happens to the PPF when technological change overwhelmingly favours theproduction of computers? v. What happens to the PPF when the economy discovers an improved technology forproducing shoes? vi. Assume now that the sacrifice ratio is greater than 1, show what will happen to the…
- 500 400 300 200 100 Pumpkin 100 200 300 400 500 Wonderland produces and consumes two goods, pumpkins and sweet potatoes, by using two inputs, labor and capital. The production possibilities frontier of Wonderland is shown above. Which of the following combinations of pumpkins and sweet potatoes is NOT a combination which is "definitely better than the autarky consumption combination (A)"? O 300 units of pumpkins and 200 units of sweet potatoes 100 units of pumpkins and 500 units of sweet potatoes O 300 units of pumpkins and 300 units of sweet potatoes O200 units of pumpkins and 300 units of sweet potatoes$ aved Refer to Figure 2. Consider the following movements: -from point Vto point W -from point W to point Y -from point Y to point Z Which of the movements listed above represents advancements in technology with respect to both plastic production and food production? 1) conly 2) b and c only 3) a, b, and c Plastic products 4) b onlyAn economy produces two goods ,X and Y .lt uses two means of production, labour and capital. A unit of labour can produce either 1unit of X or 4units of Y (or linear combination of the two).A unit of capital can produce either 4units of X or 1unit of Y (or linear combination of the two)there are 100units of each means of production. (i) Draw the production possibility frontier of the economy when the two goods can only be produced by a mixture of both factors. (ii)What will be the opportunity cost of X if the economy produces 50units of X ? (iii) Given that the production technology is linear ,will the opportunity cost of X remain unchanged when we produce 90units of X ? (iv)Briefly explain the difference between the PPC with a constant opportunity cost and the PPC with an increasing opportunity cost as more output of one good is produced. Use a well labeled diagram to explain your answer?