A firm's production is Q= 60L-0.02L² Where Q denotes output and L denotes the size of the workforce, calculate the value of MPL when (i) L = 10 (ii) L = 100
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- What is the difference between a fixed input and a variable input?Complete the table directly below by calculating MP and AP. Inputs ofL TP MP AP 0 01 152 343 514 655 746 807 838 82 Plot the TP, MP and AP and explain in detail the relationship between eachpair of curves. Explain why PM first rises, then declines, and ultimatelybecomes negative.Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.
- Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.According to the law of diminishing returns, if a factory keeps adding more workers while keeping the amount of machinery constant, eventually: 0000 Total output will start to decrease. Output per worker will start to increase. The additional output generated by adding another worker will start to decrease. The factory will become more efficient.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.)
- 100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.Cost curves Egidio Binaccio designed an ancestry app that allows people to connect with long lost Italian relatives. Egidio notices the following relationship between the number of hours he schedules and the number of downloads (sales) he gets. Below is a production function, for Egidios current company set up. NUMBER of LABOUR DOWNLOADS HOURS B) 10 C) 20 30 40 50 60 70 80 90 100 110 120 130 140 6.50 11.00 14.50 17.50 20.50 23.75 27.50 32.00 37.50 44.50 53.50 65.00 79.50 97.50 TVC TC MC AVC Suppose the firm can hire all the labour it would ever want at the going wage of $8 per labour-hour. The firm's total fixed costs are $64 per day. A) ATC Fill in the table showing total variable cost (TVC), total cost (TC), average variable cost (AVC), average total cost (ATC), and marginal cost (MC). [Remember: Marginal cost should be entered midway between rows of output.] On a graph with DOWNLOADS (per day) on the horizontal axis, draw the three "per-unit" cost curves, AVC, ATC, and MC. [Note…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…A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?Derive formulae for the marginal products of the three inputs in the produc- tion function Q = 40K03L0.3R04. %D
