Given the equation of Q = min(4K,8L), how much output is produced when 2units of labor and 5 units of capital are employed? answer must be a whole number only
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- What is the difference between economies of scale, constant returns to scale, and diseconomies of scale?What is a production function?(i) Find the rate of change of the function f(x) =x + 2/ 1 − 8x with respect to x when x = 1.(ii) The number of units Q of a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure, whereK(t) =2t4 + 3t + 149 / t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be producedat this time?(b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?
- 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.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?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 an a trawler is a function of the crew size assigned to operate the boat. Based on past data, consider the following production function identifying the relationship between output and labor input. You may assume that capital is fixed at 10 units.Labour Input (No of. Workers) (L) Total Product TPL (Q). From the table below :-(a) Calculate APL and MPL. (b) Graph APL and MPL. Do they have the expected shape? (c) On your graph, identify the three stages of production Labour input (No of Workers) (L) Total Product TP L (Q) 0 0 1 80 2 170 3 300 4 450 5 540 6 620 7 700 8 770 9 830 10 880 11 920 12 950 13 970 14 980 15 985 16 988 17 988100VKL, 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.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…
- 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.)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.