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Jolene has a production function 4?1 + ?2. If the factor prices are £12 for factor 1 and £2 for factor 2, how much will it cost her to produce 30 units of output? Use lagrange to solve this
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- Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. 1. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the L(q) and K(q)?Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the long run total cost function, C(q)? Sketch it on the diagram.Prunella raises peaches where L is the number of units of labor she uses and T is the number of units of land she uses. Her output is f(L,T) = LT bushels of peaches. If the cost of land is 6 and the wage for labor is 5, find the cost minimizing amount of labor to use subject to the constraint that output must be 673 bushels. Round your answer to the second decimal place, e.g., 12.345 12.35. ==
- Amy wants to open a coffee shop and has already rented a coffee retail space on Bloor Street, signing a lease for three months, which includes her expresso-making equipment. The rent is $900 per week and the wage for barristas is $16 per hour. Amy can legally keep her shop open up to 100 hours a week. The number of expresso drinks q Amy’s barristas can make in an hour given the capital on hand, and assuming she doesn’t run out of beans or cups, is given by q = 15L.5 where L is the number of barristas currently working. Amy can provide 50 hours of barrista labor herself instead of hiring a worker if she wants to reduce labor costs, and she could also work 50 hours a week running the coffee shop across the street for $25 an hour. The typical price of an expresso drink is $7, which Amy takes as given since there are many other coffee shops in the neighborhood. The cost of the materials M (cups, beans, and milk) that go into each drink sold is $2.50, and Amy’s coffee bean and cups…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 = 2.4Prunella raises peaches where L is the number of units of labor she uses and T is the number of units of land she uses. Her output is f(L,T) = LT bushels of peaches. If the cost of land is 18 and the wage for labor is 13, what would be the slope of an iso-cost line, where total cost is $500. Tis on the vertical axis. Don't forget the negative sign! Write answer to 2 decimal places, e.g., 0.93
- 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.Does the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?Q₂ A production function is given by q = 500L + 700K. The price of capital is $120 and the price of labor is $100. If the firm wants to produce 1,400 units of output, how many units of labor should it use? Your Answer: Answer
- You are running a small factory that uses labour (L) and capital (K) to produce output (Q). Your production function is Q space equals space 10 L to the power of bevelled 1 half end exponent K to the power of bevelled 1 half end exponent For every unit of labour you use you have to pay a wage of w = $ 20 and for every unit of capital you use you have to pay a rental rate of r = $5. You've signed a contract that you will produce Q = 700 units of output. If you minimize your costs, what amount of labour (L*) should you use?Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}.If he uses 1 kg of wool and 3 hours of labour, he can produce 1 t-shirt. 1. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the optimal bundle of that he can produce in order to minimise costs? Draw the isocost lines.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
