The production function is f (L, M ) = 5L1/2M 1/2, where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied and if the cost of labor is $9 per unit and the cost of using machines is $64 per machine, then what is the total cost of producing 12 units of output?

Suppose Z=0, Y=9. Please solve in details.

Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.

Emma sells hot chocolate outside of Yankees baseball games. They have two inputs in the production of hot chocolate: (hot chocolate mix (x1, measured in kg) and labour (x2, measured in hours. The production function for hot chocolate (in liters) is: f (x1 , x2) = (x1)1/3(x2)1/3 A) Does this firm have constant, increasing or decreasing returns to scale? The cost of hot chocolate mix is w1, and the cost of labour is w2. If Emma produces "y" liters of hot chocolate the cheapest way possible, then B) How many kilograms of hot chocolate mix would they use? C) How many hours of labour? D) What is the cost function of producing this much hot chocolate?

Consider the following cost function (C): C= 0.25q3 - 4q? + 75q + F. The equation for average cost (AC) is: AC = |. (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 ^ character.) The equation for variable cost (VC) is: Vc=. (Properly format your expression using the tools in the palette.) The equation for marginal cost (MC) is: MC =. (Properly format your expression using the tools in the palette.)

Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?

Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph TPL, APL, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (iii) the maximum value of MPL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…

Which of the following production function would exhibit increasing returns to scale? f(K, L) = (K+ L)1/2 f(K, L) = K + L f(K, L) = K1/4+ [1/4 Of(K, L) = KIL None of the above

A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $20 per worker-hour and the cost of capital is $10 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 28,800 plastic bins? Hint: The marginal products are MP, = K and MPg = L.

Total Cost = C(x) = 0,005x^3 - 0,49x Lnx +5x Find : a. Average Cost Function b. Average Cost Minimum