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Q). #1 The following table describes the production function of a particular farm with avocado plantations: Labor TP - Type A TP - Type B Field (tons) Field (tons) 1100 800 1750 1500 2100 2100 2300 2600 2400 3000 2450 3000 2450 2900 a. Calculate the average output and the marginal output of the workers in each field separately. b. Calculate the maximum output of the farm if the number of workers is: 2, 4, 9. c. What is the marginal output of the workers when their number is: 2, 4, 9? d. Outline a marginal output curve of the workers. e. Assume that the farms employed 11 workers. In addition, the wage is determined by the last worker allocated. What would be the farm's profit if the price of the product is 10 $ per unit?Marginal Product Marginal product of labor (MPL) is the change in output resulting from employing an added unit of labor. In other words, it is the change in the total product that results from adding a unit of work (one worker, one hour, etc.) It can also reflect the contribution of the last (marginal) unit of labor. Change in Total Producr AQ ATP MP = Change in Labor AL AL 4Q Q1 -20 AL -L1 - Lo Example #2 Assume a farmer that has a field for growing wheat. The constant production factor is the field area (land), and the workers are the variable factor of production. The following table illustrates the expected output according to the change in the number of workers (input). Compute AP and MP and plot them on a graph. Q=Total Product Average Product |Marginal of wheat Variable input in tons AP product Labor (L) TP 0 9 24 42 60 75 87 97 101 101 10 95 3Q=Total Product of wheat in Variable input tons Average Product Labor (L) TP AP Marginal product 0 9 9:1=9 9-0-9 24 24:2-12 24-9-15 42 14 42-24=18 Aw 60 15 60-42-18 75 15 75-60=15 87 14.5 87-75-12 97 13.7 97-87=10 101 12.6 101-97-4 101 11.2 101-101=0 10 95 9.5 95-101=-6 The MPL curve intersects the APL curve at its maximum point. It has 3 areas: rising marginal output, then decreasing (but positive) marginal output and then negative marginal output. In the latter area productivity begins to decline. 120- 100- 80 - 60- 40- 20- 2 3 4 5 10 MP - TP AP 4Allocation of production factors under diminishing marginal product Let assume a farm that has two types of fields: Field A field and one type B field (fixed factors of production) as well as workers (variable factor of production). TP - TP - Field A Field B 1 100 800 1750 1500 2100 2100 2300 2600 2400 3000 2450 3000 2900 a. Assume that L=5. Show the labor allocation that guarantees Max TP. b. Compute the Marginal product of the 5 workers. c. Compute the marginal product of a Type-A field d. Compute the marginal product of a Type-B field (a) We utilize the MP of each field to allocate workers. Marginal TP - Marginal Product TP - Product Field A MPA Field B 0 1100 100-0=1100 1 800 2 1750 1750-1100=650 4 1500 700 2100 350 2100 500 2300 200 2600 500 2400 100 3000 400 2450 50 3000 0 2450 0 2900 -100 The first worker is placed in field A because his/her marginal production is higher than in placing him in field B: 1100> 800. The second worker is placed in field B: 800> 650. 6The allocation of production factors will be according to the maximum marginal production that can be achieved. TP resulting from L=5: TP = 1100 + 800 + 700 + 650 + 600 = 3,850. (b) The marginal output of all workers is basically the marginal production of the last worker. Therefore, the marginal production of the workers is 600. The last allocated employee contributed 600 to the total product. (c) Marginal production of type-A field: In order to find the marginal productivity of the fields, it is necessary to first find the allocation of workers: Two workers will be assigned to Field A. Three workers will be assigned to Field B. Loss of output from cancellation of field A: -1750 Allocating the two workers who worked in Field A as workers in field B: +500 + 400 = 900 Sum -850 Therefore, the marginal output of a type A field is 850. (d) Marginal production of type-B field: Originally, two workers were assigned to Field A and three workers were assigned to Field B. Loss of output from cancellation of field B: -2100 Allocating the three workers who worked in +350 + 200 + Field A as workers in field B: 100 = 650 Sum -1450 Therefore, the marginal productivity of a type B field is 1,450.Now, let assume that there is L=5, 5 Type-A fields and one Type-B field. (a) Show the allocation of workers (b) What is the Max. production? c. What is the marginal product of a Type-A field Answers: (a) One worker will be assigned to each of the five type A fields. No workers should be assigned to field B. (b) TP = 5 . 1100 = 5,500 (c) The marginal productivity of L=5 is 1, 100. (d) Marginal productivity of a Type A field is: Loss of output from cancellation of field A: -1100 Allocating the worker who worked in Field A as workers in field B: +800 Sum -300 Therefore, the marginal output of a type-A field is 300