A manufacturer has $600 to spend on the production of a certain product and knows that if "x" units of capital and y units of labor are allocated to production, then "P" units will be produced with P(x.y)=120x4/5y1/5, Assume that each unit of capital costs $3 and each unit of labor power costs $5. Use Lagrange multipliers to find how many units of capital and labor power should be used in order to maximize output.
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- The table below shows the marginal benefit for various inputs. Assume that each level represents a $100 investment, and answer the following questions. (a) If you have an unlimited budget, how much would you spend on each input? Explain.(b) Now, assume you can spend a maximimum of $500. What would you spend on each inputnow? What order would you buy them in?(c) Finally, assume you can borrow as much as you want with an interest rate of 10%. How muchwill you borrow and how will you spend it if you have to pay back the loan within 1 year?Specify 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.Trey works as a waiter for Puff & Stuff catering for a wage of w 11. In addition to his %3D labor income from waiting, Trey makes supplemental income with his household production time by streaming video games on Twitch. He doesn't have any unearned income (V=0). Trey's preferences over consumption and household production are given by the utility function below: u (H, C) = 2\H + VC Assume Trey has 16 hours each day to split between household production and consumption, if he spends 10% of his time at home streaming and earns an hourly rate of P = 7, what will be his optimal allocation of household production? (hint: assume that Trey's utility-max condition remains unchanged and his supplemental income will only impact his budget constraint)
- As the price rises, the quantity demanded by the buyer will decline and the quantity supplied by sellers will increase until it reaches the point when there is no shortage. Therefore, identify and explain the point where there is no shortage happen. Production means the process of using factors of production to produce goods and services. The inputs bought and used in the production of a given product are classified into four factors of productions. Describe the FOUR (4) factors of production with examples Ans allElsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = 4BW where B is the amount of bananas she consumes and Wthe amount of water. Her production function for bananas is B=Lg where Lg is the amount of labour time she devotes to bananas. Her production function for water is W = Lwwhere Lwis the amount of labour time she devotes to water. If the total time she has available is 70, what should she do to maximize her utility? (Enter your answers in whole numbers.) LB= Lw=[Assume an economy produces 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 laws 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 forgoing assumptions , drawthe economy's production possibility frontier on hindsight of the relevant assumption and why the points outside the frontier unattainable?.
- 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…Consider the production function of Firm Y below utilizing inputs labor (L) and capital (K) in production. The fırm faces the fixed price for labor and capital at 5 per unit and 10 per unit, respectively. Y 10K1.5L0.5 2. Using Lagrange Multiplier Method, calculate the cost-minimizing values of L, K, and C of Firm Y if it decides to produce 1,000 units of good Y. Graphically illustrate the expansion path of Firm Y if it decides to double its target output.17. 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.
- 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 andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions:vi. Assume now that the sacrifice ratio is greater than 1, show what will happen to the shape of the production possibility frontier.Consider the production problem discussed in class in which 24 labor hours and 4 machinehours are to be allocated between food (x) production and wine (y) production. Suppose theproduction functions for x and y are as follows:Also, suppose the preferences of the agents are given by:Finally, suppose the MRT is given bywhere x and y denote, respectively, the aggregate quantities of food and wine produced.For each of the following allocations, determine whether they are (i) feasible and (ii) Paretoefficient. If they are inefficient, explain intuitively how it is possible to make someone betteroff without making the other person worse-off.a. ((14,2),(10,2),(5,10),(23,18))b. ((8,2),(16,2),(5,14),(11,18))c. ((14,2),(10,2),(14,21),(14,7))The graph below is Mendork's production possibility curve for the only two goods that it produces: quirks and quarks. Quantity of Quarks 800 700 600 500 400 300 200 100 2 4 6 8 10 12 14 16 18 20 Quantity of Quirks Note: If the image does not appear, right-click on the placeholder and choose Show picture or View image. If Mendork's current production is at point A, what is the (approximate) cost of producing one more quirk? a) 50 quarks B b) 100 quarks c) 200 quarks d) One more quark e) 25 quarks