Homework 3

I need all four parts answered. Also, the answer requires diagrams. The previous answer had no diagrams and read like it was done exclusively with AI.

15. Apple uses labour and machines to produce iPhones according to the production function y = LM, where L is the number of units of labour used and M is the number of machines. The cost of labour is w₁ = 4 per unit and the cost of using a machine is wM = 16. Apple faces a fixed cost of F = 25 for renting its factory. Given these input prices, Apple chooses how much labour and machines to employ in order to minimize the cost of producing any given amount of iPhones y. Apple is therefore solving a cost-minimization problem. (a) If Apple is cost-minimizing, how many workers will it use for each machine? That is, find the number of workers per machine that Apple will employ. (Hint: setup the tangency condition.) Continuing to assume that Apple produces any given number of iPhones y in the cheapest way possible, use the equation defining the number of workers per machine from part (a) and Apple's production function to find expressions for the cost-minimizing choices of labour and machines…

A factory that you are managing has an hourly production process that can be represented by the following Cobb-Douglas production function: Q = (K^0.25)(L^0.25.) The price of one unit of capital per hour is $10 and the price of one unit of labour per hour is $20. a) Find the optimal amount of labour and capital that you will be using to produce 100 units of output, b) Compute the total cost of producing 100 units of output. c) What have you learn from doing or thinking about this problem?

Suppose that the production function for a phone is ? = 20K^0.5L ^0.5 . The marginal product of labor is 10(k/l)^0.5 , and the marginal product of capital is 10(L/K) ^0.5 . Suppose that labor can be hired for $6 and capital can be hired for $9. a. When the firm is producing 49 units at lowest cost, what will the firm’s marginal rate of technical substitution be? b. Solve for the lowest-cost combination of labor and capital that will allow the firm to produce 49 phones. Fractional units of labor and capital are allowed. c. What is the minimum cost of producing 49 phones?

Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q= 4K¾L where q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. (K For this production, MP, L and MP = 3 K K The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost What ratio of capital to labor minimizes Miguel and Jake's total costs? (Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital and labor.)

Exercise 21.1 A firm has weekly production function q(k, 1) = k!/471/2, and the unit weekly costs for capital and labour are v = good. Find the minimum cost of doing so. 20 and w =10. The firm wishes to produce 200 units a week of its

Q3) A chair manufacturer hires its assembly-line labor for $30 an hour and calculates that the rental cost of its machinery is $15 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 3 hours of labor for each hour of machine time, is it minimizing its costs of production? If so, why? If not, how can it improve the situation?

As a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500, the cost for one capital is $250. If the firm has a budget of $7500 to produce, what is the firm's optimum output 250 200 100 150

Suppose a firm uses capital​ (K) and labor​ (L) to produce widgets according to the production function Q​ = K​^(1/4)L​^(1/4) ​ = ​(KL)^(​1/4)​, where Q is output. The goal in this problem is to find the​ firm's total and marginal cost functions. In order to derive the cost​ function, the first step is to find the location of the​ cost-minimizing bundle on any given isoquant. To get a numerical​ answer, recall that the slope of an isoquant is ​-MPL​/MPK ​ (K is on the vertical​ axis). Using​ calculus, it can be shown that this slope formula reduces to​ -K/L. For​ example, consider the input bundle with K​ = 8, L​ = 2 on the isoquant with Q​ = 2​ (note that 2​ = 16​1/4 ​ ). The formula indicates that the slope at this point is​ -4 =​ -8/2. In​ fact, the formula tells us that regardless of which isoquant an input bundle is​ on, the slope will be​ -4 as long as the ratio of K to L is​ 4:1. ​ Similarly, the isoquant slope will be​ -1 whenever the ratio of K to L is​ 1:1.   In answering the…

I haven't been able to answer this correctly, and neither has anyone I've shown, can you help me with this?

Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q = F(L, K) Q = 10L0.25 K0.25 where Lis their number of workers and K is units of capital. The wage rate is $160 per week and a unit of capital costs $100,000 per week. Suppose that when initially producing 10 square feet a week, they use 0.04 unit of capital. a. What is their short-run cost of remodeling 100 square feet per week? Instructions: Round your answer to the nearest whole number. b. What is their short-run average cost of remodeling 100 square feet per week? Instructions: Round your answer to the nearest whole number. c. What is their long-run cost of remodeling 100 square feet per week? Instructions: Round your answer to the nearest whole number. d. What is their long-run average cost of remodeling 100 square feet per week? Instructions: Round your answer to the nearest whole number. %24 %24

Suppose that the production function for Hannah and Sam's home remodeling business is Q=f(L,K) Q=1040.2K0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places.

Question 18 Consider a firm that has production function f(L,K)=4L2/3K1/3. What is the expression for this firm’s Marginal Product of labor? MPL(L,K)= 2K2/3/3L2/3. MPL(L,K)= 2K2/3/L1/3. MPL(L,K)= 2K1/3/3L1/3. MPL(L,K)= 5K2/3/3L2/3. MPL(L,K)= 8K1/3/3L1/3.

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The table below shows the weekly relationship between output and number of workers for a factory with a fixed size of plant. P= 10$: w=100$  a) Calculate the marginal product of labor. b) At what point does diminishing returns set in? C) Calculate the average product of labor. D) Find out optimum level of variable input usage

Suppose that the production function for Hannah and Sam's home remodeling business is            Q = F(L,K)            Q = 10L0.1K0.4.Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $1,000 per week.a. What is the least-cost input combination for remodeling 400 square feet each week?      Instructions: Round your answers to 2 decimal places.      units of labor and  units of capital.  b. What is the total cost?         Instructions: Round your answer to 2 decimal places.    $  .revised jrl 08-11-2011

Suppose a firm is producing 2,475 units of output by hiring 50 workers (W = $20 per hour) and 25 units of capital (R = $10 per hour). The marginal product of labor and marginal product of capital are 30 and 15, respectively. Is the firm minimizing the cost of producing 2,475 units of output? Explain.

Maximizing profit with isoprofit curvesSuppose that you are starting up a lawn-raking business. All of your workers are required to supply their own rakes, so the only cost to you is hiring labor at an hourly rate. Suppose that the market price of raking someone's yard is $24 per lawn and the hourly wage is $18 per hour. The following graph shows the production function (PF) for your business.