Q4 The output of a production process, Q, is given by the function KL 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. 05
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- 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.(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?
- 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.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 .What is the difference between economies of scale andeconomies of scope? How do firms consider these wheninvesting in processes?
- Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by the following function. S- 20100.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min s.t. -55,000 L.C20 (b) Solve the optimization problem you formulated in part (a). (Hnt: When using Excel Solver, start with an initial L>O and Co. Round your answers to the nearest integer.) at (L. C) =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…
- 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.You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled 1.Find the ranges of the three stages of production. 2.Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above 3.At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? 4.Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…This one should test whether you really understand this stuff by changing the story just enough that it won't be obvious what equation from your notes you need to use or how to apply it. You may need to think about it carefully. Input only integers except for the last question. Consider a beekeeper. The beekeeper has the following production function where the input is the number of hives and the output is quantity of honey produced. Beehives 1 2 3 4 5 6 7 8 9 10 11 Honey 12 23 33 42 50 57 66 71 75 78 80 The cost of installing a beehive is $100 and the price of a unit of honey (whatever that is...) is $20. Also each beehive increases the output of apples at a nearby apple orchard by $40. 1. What is the efficient…