The firm Greench produces T-shirts. The production function is given by the following: T-shirts = min(83 L, 17 K) The price of labor is $36, the price of capital is $43, the price of T-shirts is $100, and Greench's costs are $2516. What is the optimal amount of capital?
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- 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?Write down the problem the car manufacturer solves to find the levels of 'K' and 'L' that minimize cost. What two equations are used to solve it?A9
- Hi, please help with the questionA firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L1/2M1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400and another isocost line showing combinations that cost $200.2. Suppose that the firm wants to produce its output in the cheapest possible way. Find thenumber of machines it would use per worker. (Hint: The firm will produce at a point wherethe slope of the production isoquant equals the slope of the isocost line.)1. The production function for the personal computers of DISK, Inc., is given by q = 10K0.5L0.5,where q is the number of computers produced per day, K is hours of machine time, and L ishours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function q = 10K0.6L0.4. a. If both companies use the same amounts of capital and labor, which will generatemore output?b. Assume that capital is limited to 9 machine hours, but labor is unlimited in supply. Inwhich company is the marginal product of labor greater? Explain.
- 4. Ikea Inc., a home remodeling business. The number of square feet they can remodel in a day is described by the Cobb-Douglas production function Q= F (L,K)= 4K5L0.5 where L is their number of workers and K is units of capital. The wage rate is $5 a day, and a unit of capital costs $20 a day. What is their minimum cost input combination for remodeling (Q=200) 200 square feet a day? What is the total minimum cost level? (15p)4. Ikea Inc., a home remodeling business. The number of square feet they can remodel in a day is described by the Cobb-Douglas production function Q= F (L,K)= 4K"L* where I. is their number of workers and K is units of capital. The wage rate is $5 a day, and a unit of capital costs $20 a day. What is their minimum cost input combination for remodeling (Q=200) 200 square feet a day? What is the total minimum cost level?A firm's production function is q = 26x^0.33y^0.67, where x and y are the amounts of factors x and y that the firm uses as inputs. If the firm is minimizing unit costs and if the price of factor x is 6 times the price of factor y, the ratio in which the firm will use factors x and y is closest to. A. x/y = 0.08 B. x/y = 0.25 C. x/y = 0.5 D. x/y = 2.4
- A firm has the following production function: Q=f (L/K). It must pay $20 per hour of labor and rents its fixed inputs (K) for $30 per unit. Complete the following table and answer the questions that follow: Units of fixed input K Labor Hours (L) Output (Q) TFC TVC TC AFC AVC ATC MC 3 0 0 90 0 90 0 0 0 0 3 1 4 90 20 110 2.25 1/2 11/4 1/2 3 2 90 90 40 130 1 11/25 13/9 10/43 3 3 160 90 60 150 9/16 3/8 15/16 2/7 3 4 200 90 80 170 9/20 2/5 17/20 1/2 3 5 230 90 100 190 9/23 10/23 19/23 2/3 3 6 250 90 120 210 9/25 12/25 21/25 1 3 7 260 90 140 230 9/26 7/13 25/26 2 3 8 265 90 160 250 18/53 3/5 249/265 4 Plot AFC, AVC, ATC, and MC on a graph. Explain what happens to each one as output increases and why.A firm can manufacture a product according to the production function Q = F(K, L) = K3/4 L1/4 a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. How does the average product of labor change when the firm uses 256 units of labor? b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 81 units. Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor. c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit of output and can hire labor at $50 per unit of labor, how many units of labor should the firm hire in order to maximize profit7. A fast-food company in Hermanus has the following cost function: TC = 10 + 3K + 2L, where L is the number of labour hours and K is the number of machines they have to use. They have a production function of Q = 2KL, where Q represents the number of meals produced per day. The company has to make at least 75 meals every day. Using the Lagrangian method of production optimization, calculate the optimal number of labourers and machines needed to meet this quota. (6)
