17.4 A firm uses two inputs to produce a single product. If its production function is Q = x/y1/4 and if it sells its output for a dollar a unit and buys cach input for $4 dollars a unit, find its profit-maximizing input bundle. (Check the second order conditions.)
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- 3.10. A firm uses two inputs to produce a single product. If its production function is Q = x¹/4y¹/4 and if it sells its output for a dollar a unit and buys each input for $4 dollars a unit, find its profit-maximizing input bundle. (Check the second order conditions.)6 A production function is given by f(x1,x2)=(max{x1,x2})^0.5. Prices of inputs are p1=10 and p2=20. What is the lowest cost of producing 10 units of output?
- Problem 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…2 The company Shirts Galore has figured its total cost of producing and sclling x units of T-shirts per month is given by the equation C(x) = 120 +2.5x-0.0002r. a) Write a rational function to represent the average cost of producing and selling a shirt. b) If the production level is 1200 shirts per month, find the average cost of producing and selling a shirt. c) If the shirts are sold for $7.98 a shirt, what is the profit realized on producing and selling 1200 shirts per month? d) What price must be charged when selling the shirts for a profit of $7368 to bc made on 1200 shirts in one month? * A large company is considering changingNot use ai please
- Which of the following profit functions exhibits a linear production function? A.p= Px K0.75L0.50 - 20L - 35K B. p = Px min (2L, 5K) - 20L - 35K Cp= Px (3K + 4L) - 20L - 35K D. p = Px (3K05 + 4L05,1/02 - 20L - 35Kam. 154.A 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.)
- Y6 questions1. A firm produces TVs and ovens witha joint cost function that takes the form:C(x,y) = 3x^2 + 2y^2 + 2xy where x and y are the firm's output of TVs and ovensrespectively. Suppose the cost function is subject to the constraint on the total output ofthe firm in the form 2x + y = 35.a) Find the optimum values x and that minimize the firm's total cost.b) Check your answer in (a) by using the bordered Hessian matrix.c)Determine the optimum value of the Lagrange multiblier À. Interpret your answer.2. A competitive firm uses two variable factors to produce its output, with a production function q min{x₁, x₂}. The price of factor 1 is $8 and the price of factor 2 is $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x₁. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no butput. What is the smallest integer price that would make a firm willing to produce a positive amount? b. d. $44 $41 $29 $13 $211 A smartphone repair firm in Boston has a production function for producing phone repairs, q, defined as, — 4 -L1/2K 1/2, where L is labor measured in hours worked, and K is the number of useful tools used in the repair process. The market wage for a phone repairperson, w, is $25 per hour. The tools could be sold at a secondhand market for $4 (r). Find the (variable) cost function:. Submit your answers as a single PDF. Please try and keep solutions tidy.
