4. A firm has a linear production function Q = 16L + 8K. The price of labor, w, is $6 per unit and the price of capital services, r, is $2 per unit. Find the optimal input combination given that the firm wishes to produce 320 units of output. Illustrate your answers with a diagram.
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- 24. A specific production process can be represented by the production function, f(x1, x2) = (x 1/2 + x 1/3) 3. A. How much x₁ could the firm give up if it wanted to use 1 extra unit of x2 and still wanted to produce an identical level of output? B. Labeling everything and being precise, draw the isoquant corresponding to q = 4. = 9. C. On the same graph, draw the isoquant corresponding to q D. Between the isoquants you just drew, does the production technology display decreasing, increasing, or constant returns to scale? E. Analytically determine whether the production process has global returns to scale that match your local results from part D. Recall that in order to claim global returns to scale, your result must hold for ALL possible values of x1 and x2.***There are FOUR parts to the question, all based around the same given data...please answer and explain each and note where graphs are needed*** Given: A farmer raises apples using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor? d. In the long run, the farmer can change both his…Present a graph of the following. Label your graphs completely1. Using the isoquant map and isocost, show that combination M is the optimum combination of inputs and not combinations E and L.
- .2. Tiva has a crafts store that makes jewelry using beads (B) and copper (C). Her productionfunction for jewelry is given byQ = B0.4C0.4Suppose she can buy beads and copper at prices PB and PC, respectively.(a) Calculate Tiva’s marginal rate of technical substitution between B and C.(b) Does this production function have increasing, constant, or decreasing returns to scale?Explain. (c) Set up the cost minimization problem you would use to calculate Tiva’s cost functionC(Q) in Lagrangian form. (Note: You do not need to solve it or derive first orderconditions.Suppose Tiva decides to branch out in her jewelry offerings by getting a 3D printer. The costof producing new 3D printed jewelry isC(Q) = 25 + Q24For the rest of this problem, assume Tiva can produce fractions of jewelry, don’t worry aboutrestricting your answers to whole numbers.(d) Compute Tiva’s marginal cost and average cost of production for 3d printed jewelry.(e) Explain why she will shut down when the market price falls…Gopher Excavators produces shovels in a small factory and sells the shovels in a competitive market. The following table shows the company's production function: Output (Number of workers) (Shovels) Labor 1 100 195 275 4 340 380 Use the blue points (circle symbol) to plot the production function for Gopher Excavators on the following graph. 40 Producion Function 340 100 130 40 LABOR (Number of workana) Calculate the marginal product of labor (MPL) of each worker, and then plot the MPL curve on the following graph using the blue points (circle symbol). Note: Remember to plot each point halfway between two integers. For example, when the number of workers increases from 0 to 1, the MPL of the first worker should be plotted with a horizontal coordinate of 0.5, the value halfway between 0 and 1. Line segments will automatically connect the points. (genoygl indinoA commercial fisherman notices the following relationship between hours spent fishing and the quantity of fish caught: Hours Quantity of Fish (in pounds) 0 hours 0 lb. 1 10 2 18 3 24 4 28 5 30 What is the marginal product of each hour spent fishing? Use these data to graph the fisherman’s production function. Explain its shape. The fisherman has a fixed cost of $10 (his pole). The opportunity cost of his time is $5 per hour. Graph the fisherman’s total-cost curve. Explain its shape.
- 6. The Miller Company is trying to determine the combination of inputs to produce a specific volume of bar stools ordered. The production function for the firm is given: Q = 14LK? The wage of a worker is $80/day and the price of a machine is $240/day. If they need to produce 4,536 bar stools per day: a. What is the optimal combination of Labor and Capital, i.e. find the cost-minimizing combination of inputs to produce 4,536 bar stools? b. What is the total cost of using the inputs found in part a?Question 8 of 13 The following diagram depicts the production function of the farmers, where diminishing average product of labour is assumed. At A the average product of labour is 500,000/800 = 625 kg of grain per farmer. At B the average product of labour is 732,000/1,600 = 458 kg of grain per farmer. If you know that for 2,800 farmers the grain output is 894,000kg, then which of the following is/are correct? Kilogrammes of grain produced (thousands) 900 800- 700- 600- 500 400- 300- 200- 100- 0 0 400 800 B 1,200 1,600 Number of farmers 2,000 2,400 2,800 OA. The average product of labour when the labour input is 2,800 is 300. OB. The decreasing slopes of the rays from the origin to the production function along the curve indicate the decreasing average product of labour. OC. If the production function curve is an upward-sloping straight line, then there is no diminishing average product of labour. OD. It is possible that initially there is an economy of scale: for example, going from…6. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q = K2 L12 where K is capital (for example nest boxes, cages and the like) and L is parrot food. The price of K is $8 and the price of L is $2. a. What type of production function is this? b. Does this production function exhibit constant, increasing or decreasing returns to scale? Explain. c. What is the average product of capital?