Suppose prices of labor and capital are $4 and $5 respectively. And 30 units of product A can be produced by employing just labor and capital in the four different ways of technique. Production Techniques: I II III IV Labor 3 2 4 Capital 1 3 Refer to the above table. Which technique is economically most efficient in producing A? O a) I. O b) II. O c) II. O d) IV.
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- Give the three reasons that explain why the division of labor increases an economys level of production.What is the difference between a fixed input and a variable input?A small company that shovels sidewalks and driveways has 100 homes signed up for its services this winter. It can use various combinations of capital and labor: intensive labor with hand shovels, less labor with snow blowers, and still less labor with a pickup truck that has a snowplow on front. To summarize, the method Choices are: Method 1: 50 units of labor, 10 units of capital Method 2: 20 units of labor, 40 units of capital Method 3: 10 units of labor, 70 units of capital If hiring labor for the winter costs $100/unit and a unit of capital costs 400, what is the best production method? What method should the company use if the cost of labor rises to $20/unit?
- What shapes would you generally expect a total product curve and a marginal product curve to have?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?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 correct
- 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.SCENARIO 7.7: A lawn service company has the following production possibilities. With one, two, three, and four workers, the company can mow 4, 9, 12, and 14 lawns per day, respectively.13) Refer to Scenario 7.7. Diminishing returns to labor set in with the ________ worker.A) first B) second C) third D) fourth14) Refer to Scenario 7.7. The average product of labor with four workers isA) 3. B) 3.5. C) 4. D) 14.15) If the marginal product of labor is less than the average product of labor, then theA) marginal product must be increasing. B) average product must be decreasing.C) marginal product must be decreasing. D) Both B and C3. Theo employs labor at a competitive wage (W) of $3 per unit, and he employs capitalat a competitive rental rate (R) of $6 per unit.a. State the cost-minimizing rule. You must provide both a written statement of it, and state it as anequation.b. At Theo’s current combination of labor and capital, the marginal product of labor (MPL) is twiceas large as the marginal product of capital (MPK). Is Theo currently employing the optimal ratio oflabor and capital? If not, how should he adjust his hiring of labor and/or capital? Explain.
- 1. Given the following production function Q = 20L2K and the unit prices of labor and capital to be Birr 48 and 12 respectively, then a. What combination of labor and capital maximizes output with a cost of Birr 720? b. What is the maximum output? c. Show the output maximizing condition graphically.4. A bottling company uses two inputs to produce bottles soft drink sludge: bottling machines (K) and workers(L). The machine costs $1000 per day (r) to run and the workers are paid $200 per day (w). At the current level of production, the marginal product of the machine is an additional 200 bottles per day (MPK), and the marginal product of labor is 50 bottles per day (MPL). a. State the rule for determining the cos- efficient combinations of inputs (K & L) for the production of soft drinks. b. Given r=$1000 per day, w=$200 per day, (MPK)= 200 bottles, and (MPL)= 50 bottles, is the company operating cost-efficiently? c. What must the company do to move toward cost-efficient operation? Hint: use more labor or more machines and why?Farmer Joe’s production function is f(x1, x2) = x1/31 x1/32, where x1 isthe number of pounds of lemons he uses and x2 is the number of hours he spendssqueezing them. His cost function is c(w1, w2, y) = 2w1/21 w1/22y3/2, where y is thenumber of units of lemonade produced.(a) If lemons cost $1 per pound, the wage rate is $1 per hour, and theprice of lemonade is p, what is his marginal cost function?(b) What is his supply function?(c) If lemons cost $4 per pound, the wage rate is $9 per hour, and theprice of lemonade is p, explain in detail how these changes would affect theoriginal supply function in part (b)?