If Q = 0.5 K² L², and we use 2 units of capital and 2 units of labour, what is the average product (per unit of labour)? (Only enter the number, no units or symbols.)
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- It costs a company $58 to produce 6 units of a product and $78 to produce 10 units. Assuming that the cost is linear, how much does it cost to produce 25 units?Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is t = 50+8e-0.00005y Based on this production function, his coach also estimates that if Ben swims 20,000 yards per week, his time will be 52.94 seconds, and he will finish tenth place. If he swims 40,000 yards per week, his time will be 51.08 seconds, and he will come in third. If he swims 60,000 yards per week, his time will be 50.40 seconds, and he will win the meet. Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of swim time given y practice yards (MP) is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ MPy character.)SOLVE STEP BY STEP IN DIGITAL FORMAT The company Cielito S.A. It manufactures clothing for older adults and has a large presence in Mexico, due to the comfort and good taste of its garments. It has 60 seamstresses who work 8 hours a day; Indirect manufacturing expenses are $9,500.00 MXN. Every day Cielito S.A. produces 1,500 garments. The cost per hour of labor is $55.00 MXN. With this data, you must calculate: a. Labor or labor productivity. b. The productivity of manufacturing indirect expenses. c. The total productivity of Cielito S.A.
- The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed: CREW SIZE (NUMBEROF WORKERS) AMOUNT OF FISH CAUGHT PERWEEK (HUNDREDS OF LBS) 2 3 4 5 6 7 8 9 10 11 12 3 6 11 19 24 28 31 33 34 34 33 a. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?b. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?c. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per worker?The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed: CREW SIZE (NUMBEROF WORKERS) AMOUNT OF FISH CAUGHT PERWEEK (HUNDREDS OF LBS) 2 3 4 5 6 7 8 9 10 11 12 3 6 11 19 24 28 31 33 34 34 33 a. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?b. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?c. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per worker? Expert Solution arrow_forward Step 1 The marginal and average product of the worker or labor is useful in calculating the amount of fish that the workers can catch as well as in the real industries also. If the company calculates the average and marginal products, the company can decide on how to…*0.65 0.35 where x is the amount of labor and y is the amount of capital. The productivity of a country is given by f(x,y) = 100x (a) Compute the marginal productivities of labor and capital when x = 300 and y = 500. (b) Use part (a) to determine the approximate effect on productivity of increasing capital from 500 to 502 units, while keeping labor fixed at 300 units. (c) What would be the approximate effect of decreasing labor from 300 to 298.5 units while keeping capital fixed at 500 units? (a) The marginal productivity of labor is (Do not round until the final answer. Then round to two decimal places as needed.) The marginal productivity of capital is (Do not round until the final answer. Then round to two decimal places as needed.) (b) When capital is increased from 500 to 502 units, the approximate change in productivity is (Do not round until the final answer. Then round to two decimal places as needed.) (c) When labor is decreased from 300 to 298.5 units, the approximate change…
- a) SUPPOSE A FRIM PRODUCE OUTPUT USING THE PRODUCTION FUNCTION Q= 5KL .WAGE RATE FOR HIRING LABOR IS 200 AN HOUR AND COST OF USING CAPITAL IS 100 PER HOUR. FIND OUT THE OPTIMAL QUANTITIES OF LABOR(L*) AND CAPITAL(K*) TO PRODUCE 1000 UNITS OF OUTPUT? ALSO SHOW THE RESULT GRAPHICALLY AND INTERPRET .A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?Q4 The output of a production process, Q, is given by the function KL Q = K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. Q5 3 The equations defining a simple model of the economy are: C = 0.75Y + 18 I = 22 where C, Y and I denote consumption, national income and planned investment, respectively. Use this model to complete the following table of values and hence draw an accurate graph of C + I plotted against Y on the interval 0 < Y< 200. 100 200 C + I By drawing a second line on the diagram, calculate the equilibrium level of national income. Use your graph to explain what happens to the equilibrium level of national income when the marginal propensity to consume decreases with autonomous consumption fixed.
- Can you please start from point e), but please show your workings/calculations how did you get to the answer. Thank you!Given the production function O = min (4K, 3L), what is the average product of capital when 8 units of capital and 16 units of labor are used?The accompanying table shows the total daily output for a firm producing specialty cakes and operating with a fixed amount of capital. The cost of labour is $200 per unit per day and the fixed cost of the capital is $1500 per day. Click the icon to view the table. 24 28 8 12 16 20 Complete the last four columns of the table. Units of Labour Total Output (per day) (per day) 4 200 24 2450 28 2510 500 1200 1950 2330 2450 $ 1500 2510 $ 4800 $ 1500 $ 5600 TFC TVC $6300 $ 7100 TC MC $ 2.67 $ 1.14 $ 1.07 $ 2.11 $6.67 $ 13.33 AFC $7.5 $3 $ 1.25 $ 0.77 $ 0.64 $ 0.61 AVC $4 $3.2 $2 $ 1.64 $ 1.72 $ 1.96 ATC $ 11.5 $6.2 $ 3.25 $ 2.41 $ 2.36 $ 2.57 $ 2.23 $0.6 (Round your responses to the nearest cent.) b. Assuming that labour is only hired in increments of 4 units, what is this firm's capacity level of output? per day $ 2.83