Answer the question based on the following information: Suppose 30 units of product A can be produced by empl labor and capital in the four ways shown below. Assume the prices of labor and capital are $2 and $3, respectively. Production Techniques I II 4 3 2 3 III 2 5 IV 5 1 Labor Capital If the price of product A is $1.00, and the firm is producing efficiently the firm will realize
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- Give the three reasons that explain why the division of labor increases an economys level of production.The nation of Ectenia has 20 competitive appleorchards, all of which sell apples at the world priceof $2 per apple. The following equations describethe production function and the marginal product oflabor in each orchard:100100 2 ,2 5 25 2Q L LMPL Lwhere Q is the number of apples produced in a day,L is the number of workers, and MPL is the marginalproduct of labor.a. What is each orchard’s labor demand as a functionof the daily wage W? What is the market’s labordemand?b. Ectenia has 200 workers who supply their laborinelastically. Solve for the wage W. How manyworkers does each orchard hire? How much profitdoes each orchard owner make?c. Calculate what happens to the income of workersand orchard owners if the world price doubles to$4 per apple.d. Now suppose that the price is back at $2 perapple but a hurricane destroys half the orchards.Calculate how the hurricane affects the income ofeach worker and of each remaining orchard owner.What happens to the income of Ectenia as a whole?5 Supposing that a single consumer works for a firm, the quantity of labor input for the firm, N, is identical to the quantity of hours worked by the consumer, h - l. Graph the relationship between output produced, Y on the vertical axis and leisure hours of the consumer, l, on the horizontal axis, which is implied by the production function of the firm. (In Chapter 5, we refer to this relationship as the production possibilities frontier.) What is the slope of the curve you have graphed? PLEASE DO NOT COPY OTHER PEOPLE'S WORK AND GRAPH
- Suppose there are two inputs for production, labor and capital. The firm’s production process isdefined by the following production functiony=f(L,K).Howdoweinterpretthefirm’smarginalrateof technical substitution? a)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same cost level b)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm produces one more unit of output c)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same level of production d)a) and b) are correct e)a) and c) are correctplease asnwer the question in the image Some economists believe that the U.S. economy as awhole can be modeled with the following productionfunction, called the Cobb–Douglas production function:Y 5 AK1/3L2/3,where Y is the amount of output, K is the amount ofcapital, L is the amount of labor, and A is a parameterthat measures the state of technology. For this productionfunction, the marginal product of labor isMPL 5 (2/3) A(K/L)1/3.Suppose that the price of output P is 2, A is 3, K is1,000,000, and L is 1,000. The labor market is competitive,so labor is paid the value of its marginal product.a. Calculate the amount of output produced Y and thedollar value of output PY.b. Calculate the wage W and the real wage W/P. (Note:The wage is labor compensation measured in dollars,whereas the real wage is labor compensationmeasured in units of output.)c. Calculate the labor share (the fraction of the value ofoutput that is paid to labor), which is (WL)/(PY).d. Calculate what happens to output Y,…0. Radioco manufactures two types of radios. The only scarce resource that is needed toproduce radios is labor. At present, the company has two laborers. Laborer 1 is willing towork up to 40 hours per week and is paid $5 per hour. Laborer 2 will work up to 50 hoursper week for $6 per hour. The price as well as the resources required to build each type ofradio are given in the Table. Letting xi be the number of Type i radios produced each week,Radioco should solve the following LP:a) For what values of the price of a Type 1 radio would the current basis remain optimal?b) For what values of the price of a Type 2 radio would the current basis remain optimal?
- Class Activity •Choice land has 250 workers and produces only two goods, X and Y. Labouris the only factor of production, but some workers are better suited to producing X than Y (and vice versa). The Table below shows the maximum levels of output of each good possible from various levels of labout input a)Draw the production possibilities boundary on a scale diagram, with the production of X on the horizontal axis and the production of Y on the vertical axis. b)If the economy is producing 20 units of X and 800 units of Y, what is the opportunity cost of producing an extra 10 units of XUSE R LANGUAGE TO SOLVE THE equation The output of a production process, Q is given by the function2K^(-3)L^(5/2)/2K log4 6L^2where K and L denote capital and Inbour. Calculate the output when the capital and labour are 10 and 20 units, respectively.Digging calms by hand in Sunset Bay requires only labor input. The total number of calms obtained per hour (q) is given by :Q = 100√LWhere L is labor input per hour. A. Graph the relationship between q an LB. What the average productivity of labor in Sunset Bay? Graph this relationship and show that output per unit of labor input diminishes for increase in labor input. C. It can be shown that the marginal productivity of labor in Sunset By is given by:MPL =50√LGraph this relationship and show that labor’s marginal productivity is less than average productivity for all values of L . Explain why this is do.D. Explain the concept of diminishing returns to labor and how this concept related to increasing marginal costs.
- 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.Assume that a competitive economy can be described by a constant returns to scale, Cobb–Douglas, pro- duction function. Suppose that in this economy all factors of production are fully employed. Holding other factors constant, including the quantity of capital and technology, carefully explain how a one-time, 10-percent decrease in the quantity of labor will change labor’s share of total income?Assume that you are studying an economy which produces two goods, x and y, using two factors of production, capital K and labour L. The economy’s overall quantities of the two factors are given, and the capital intensity (the capital-to-labour ratio) in the production of y is always higher than the capital intensity in the production of x. At present there is an excess supply of y. Explain and illustrate graphically what will happen in the long run to:1) Prices of goods and production.2) factor prices and factor use intensities in each sector.