1. Suppose that a producer has the following production function: Q = KL'6 Where Q is output, and L andK are man-hours and machine-hour the two inputs used in the production process. 1A) Set up the cost minimization problem as shown in class
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- 2. A firm faces the production function 1 Q = f(K,L) = 80 [0, 4K-0,25 +0,4L-0,25] 0.25. It can buy the inputs K and L at prices per unit of 5 TL and 2 TL respectively. What combination of L and K should be used to maximize output if its input budget is constrained to 150 TL?A5Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.
- Show illustration and explain the special case of production functions "Fixed proportions production function."Question 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i. e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i. e. MPL = 1000). The price of a man- hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $25 per hour. How does this change the answer from part 1?Suppose that a firm has production function F(L, K) = L^2/3 K^1/3 for producing widgets, thewage rate for labor is w = $400, and the rental rate of capital is r = $25.a) Suppose that the firm has received an order for Q = 120 units of output. Neatly specify this firm’s costminimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.d) Determine this firm’s minimum cost of producing 120 units.e) Now suppose that the firm’s production goal is left as the variable Q. Come up with the firm’s costfunction C(Q). Show your work.
- The following is a production function. 50,000- 45,000- 40,000- Draw a graph of marginal product as a function of labor. 35,000- 30,000- 25,000- Total output (Q) 20,000- 15,000- 10,000 ng 5,000- 0+ 0 200 100 300 Units of labor (L) 400 L Q 1.) Using the line drawing tool, graph the marginal product curve from 0 to 100 units of labor. Label this line 'MP Segment 1" 2.) Using the line drawing tool, graph the marginal product curve from 100 to 300 units of labor. Label this line 'MPS Note: Carefully follow the instructions above and only draw the required objects. Does this graph exhibit diminishing returns? Explain your answer. ○ A. Yes, it does exhibit diminishing returns, because the marginal product of labor decreases. B. No, it does not exhibit diminishing returns, because the marginal product of labor is zero. ○ C. No, it does not exhibit diminishing returns, because the marginal product of labor is increasing. ○ D. Yes, it does exhibit diminishing returns, because the marginal…Hi, please help with the questionQuestion 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i.e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i.e. MPL = 1000). The price of a man-hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease?
- 1. Suppose that a producer has the following production function: Q = K³L'® Where Q is output, and L and K are man-hours and machine-hour the two inputs used in the production process. 1A) Set up the cost minimization problem as shown in class - In the cost minimization problem, the cost is minimized subject to constraint production function. It is indicated as follows: Minimize wL + rK subject to constraint Q = K3 L16 A = wL + rK + (Q-K-L6) The Lagrange f unction is differentiated by K andL to calculate the minimize the cost, and W= wage rate L=Labor R= real interest rate K = capital Q = output A= parameter coefficient 1B) Determine the cost-minimize ratio of inputs where capital costs $1 per machine-hour and labor costs $4 per lab- hour. - MRTS = Marginal product of labor Marginal product of capital Q = KL!6Problem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…a.)Suppose that labor is the only variable input in the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labor?b.)What are economies of scale? What are economies of scope? What is the difference between the two?