In a certain country, output is produced using only labor and land. The production function is Y=AXªL1-a where Y is output, X is the quantity of land, and Lis the quantity of labor. Factors of production are paid their marginal products. In this country there are 100 acres of land and 30 workers. Land earns a rent of $4,000 per acre per year. Workers are paid a wage of $10 per hour, and work 2,000 hours per year. What is the value of a?

In a certain country, output is produced using only labor and land. The production function is Y=AXªL1-a where Y is output, X is the quantity of land, and Lis the quantity of labor. Factors of production are paid their marginal products. In this country there are 100 acres of land and 30 workers. Land earns a rent of $4,000 per acre per year. Workers are paid a wage of $10 per hour, and work 2,000 hours per year. What is the value of a?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter16: The Markets For Labor, Capital, And Land

Section: Chapter Questions

Problem 13P

See similar textbooks

Similar questions

If two painters can paint 200 square feet of wall in an hour, and three painters can paint 275 square feet, what is the marginal product of the third painter?
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 we have a produ ction function for wheat Q = KL - 0.8K2 - 0.212 A. Given K = 10 Units, calculate the level of labourth at the AP reaches max andh ow Much wheatis produced at that point B. Given K = 10 at what level of labour outputreaches maximum C. How mu ch Ilevel of labor should the company hire in order to be efficient |
Imagine a firm that employs two types of workers – some with computer skills and others withno technology related skills. (i) Explain how a firm’s production function is related to its marginal product of labour, howa firm’s marginal product of labour is related to the value of its marginal product and how afirm’s value of marginal product is related to its demand for labour. (ii) Explain how the wage can adjust to balance the supply and demand for labour whilesimultaneously equalling the value of the marginal product of labour.
A es New R... 11 A A- abe X2 X2 A. St $400 A farm is currently able to produce 10,000 bushels of peanuts per season on 10 acres. Assume i adds one more acre and now is able to increase its total production to 12,000 bushels of peanuts during the growing season. Determine the marginal product of the additional acre (the 11th acre of land for this farm. MP | 1 AZ
A visiting American executive finds that a foreign subsidiary inBangladesh has hired a 12-year-old girl to work on a factoryfloor, in violation of the company's prohibition on child labour.He tells the local manager to replace the child and tell her to goback to school. The local manager tells the American executivethat the child is an orphan with no other means of support, andshe will probably become a street child if she is denied work. explain Cultural Relativist based on the statement given
Suppose that labor is the only input used by aperfectly competitive firm. The firm’s productionfunction is as follows:Days of Labor Units of Output0 days 0 units1 72 133 194 255 286 297 29a. Calculate the marginal product of each additionalworker.b. Each unit of output sells for $10. Calculate thevalue of the marginal product of each worker.c. Compute the demand schedule showing thenumber of workers hired for all wages from zeroto $100 a day.d. Graph the firm’s labor-demand curve.e. What happens to this demand curve if the price ofoutput rises from $10 to $12 per unit?
Will decrea n he fong run, assume a firm uses both labor and capital to produce 25 units of output. The marginal product of the last unit of labor being employed is 100; the marginal product of the last unit of capital being employed is 500. The wage rate of labor is $10. If the firm is minimizing the cost of producing 25 units of output, what must be the unit price of capital?
Explain how a firm’s production function is related toits marginal product of labor, how a firm’s marginalproduct of labor is related to the value of its marginalproduct, and how a firm’s value of marginal productis related to its demand for labor
An increase in the average wage also causes the labor demand curve to shift to the O A. left because the use of machines decreases, causing the average wage to increase. B. right because the use of machines increases, causing labor to become more productive. C. left because the use of machines decreases, causing the marginal cost of labor to increase. O D. left because the use of machines decreases, causing labor to become less productive. O E. right because the use of machines decreases, causing the marginal product of labor to increase.
The nation of Ectcnia has 2.0 competitive apple or--chards, all of which sell apples at the world price of$2 per apple. 11,c following equations describe theproduction function and the marginal product of laborin each orchard:Q =IOOL - L2Ml'L = 100 - U,where Q is the number of apples produced in a day,Lis the number of workers, and MPL is the marginalproduct of labcr.a. What is each orchard's labor demand as a functionof the daily wage W? What is the mar ket's labordemand?b. &:tenia has 200 workers who supply their labcrinelastically. Solve for the '""gc W. How manyworkers docs each orchard hire? How much profitdocs each orchard owner make?c. Calculate what happens to the inoome of workersand orchard owners if the world price do ubles lo$4 per a pple.d. Now suppose the price is back a l $2 per apple,but a hurricane d estroys hall the orchards. Calcu•late how the hurricane affects the income of eachworker and of each remaining orchard owner.Wl,at happens to the income of Ectcnia as…
Prunella raises peaches where L is the number of units of labor she uses and T is the number of units of land she uses. Her output is f(L,T) = LT bushels of peaches. Currently, the cost of land is 8, the wage for labor is 9, and the price of peaches is 10. Prunella is currently maximizing her profits. Which occurences would cause the quantity of labor used to decrease? O An increase in the price of peaches O A increase in the price of labor O An increase in the Marginal Product of Labor O All of the above