If x₁ = x₂ = 16, the marginal product of input 1 is two inputs is w₁ = 2 and ₂ = 1. When ₁ is increasing and 2 stays the same, the marginal product of inpu Constant O Decreasing O Increasing This production function has Constant returns to scale Decreasing returns to scale
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- Suppose there are two inputs for production, labor and capital. The firm’s production process isdefined by the following production functiony=f(L,K).Howdoweinterpretthefirm’smarginalrateof technical substitution? a)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same cost level b)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm produces one more unit of output c)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same level of production d)a) and b) are correct e)a) and c) are correctSuppose the production function for high quality brandy is given by : Q = √KL Where q is the output of brandy per week and L is labor hours per week ., in the short run K is fixed at 100, so the short run production function is Q = 10√L a. Ifthecapitalrentsfor10$andthewageare5$perhour.,writetheshortruntotalcost function. b. How much will the firm produce at a price of 20$ per bottles of brandy ? c. Howmanylaborhourswillbehiredperweek?If capital and labour are perfect complements then the marginal products of capital and labour are undefined A True Faise Question 16 A firm uses 10 units of labour and 20 units of capital to produce 10 units of output. The marginal product of labour is 0.5. If there are constant returns to scale the marginal product of labour must be 0.25 True B False Question 17 Afirm uses 10 units of labour and 30 units of capital to produce 10 units of output. The marginal product of labour is 05. If there are constant returns to scale the marginal product of labout must be 0.25 A True False
- The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1Write out an example Cobb-Douglas production function. Derive the signsfor the relationship between labor and output and for marginal product oflabor and labor, holding other inputs fixed. Explain with economic intuition.The slope of an isocost line is equal to the Select one: O a. O b. and is negative of the ratio of input prices; constant decreases as we move down the line; the ratio of the marginal products O c. is constant; the ratio of the marginal products O d. increases as we move down the line; the ratio of input prices
- (04.Suppose we are given (he constant returns to scale (CES) production function q= { ßa + aa }1/a a. Show that the marginal product of Beta is (g/B) and marginal product of Alpha (q/a)** b. Show that RTS = (2/B); I lence or otherwise shov that the ò =-1/(1-a) 1-aConsider the production function Y AK°Lta, where A is a constant, L is labour, K is capital and a 0. Which of the following is true? O The marginal product of labour is constant O The marginal product of labour is diminishing There are increasing returns to scale O There are decreasing returns to scale.2. Tiva has a crafts store that makes jewelry using beads (B) and copper (C). Her productionfunction for jewelry is given byQ = B0.4C0.4Suppose she can buy beads and copper at prices PB and PC, respectively.(a) Calculate Tiva’s marginal rate of technical substitution between B and C.(b) Does this production function have increasing, constant, or decreasing returns to scale?Explain. (c) Set up the cost minimization problem you would use to calculate Tiva’s cost functionC(Q) in Lagrangian form. (Note: You do not need to solve it or derive first orderconditions.Suppose Tiva decides to branch out in her jewelry offerings by getting a 3D printer. The costof producing new 3D printed jewelry isC(Q) = 25 + Q24For the rest of this problem, assume Tiva can produce fractions of jewelry, don’t worry aboutrestricting your answers to whole numbers.(d) Compute Tiva’s marginal cost and average cost of production for 3d printed jewelry.(e) Explain why she will shut down when the market price falls…
- In the production process, both the average product and marginal product of the variable input rise first, then fall, and then rise to infinity OFalse O True 27 WExercise 11 Question Help Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5KO.5/L0.5 - 0.5g/L 70- and MPK = 5L0.5/K.5 - 0.5g/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- -q= 280 q= 140 98 Suppose now that the firm wants to increase output to 280 units. If capital is fixed 0- in the short run, how much labor will the firm require? 70 84 L, Units of labor 14 28 42 56 112 The firm will now require units of labor. (Enter your response rounded to two decimal places.) K, Units of capitalSuppose that a firm's long-run production function where ao Which one of the following is true? -ALK The marginal products of L and K are homogeneous of degree 1.3 and the marginal rate of technical substitution is homogeneous of degree 0.3. Ob The marginal products of L and K are homogeneous of degree 1.3 and the marginal rate of technical substitution is homogeneous of degree 1.3. OC The marginal products of L and K are homogeneous of degree 0.3 and the marginal rate of technical substitution is homogeneous of degree 0.3. Od The marginal products of and x are homogeneous of degree 03 and the marginal rate of technicai substitution is homogeneous of degree zero. Oe The marginal products of and g are homogeneous of degree 1.3 and the marginal rate of technical substitution is homogeneous of degree 1. Suppose that a firm's long-run production function -r(L,K) is homogeneous of degree 3. Which one of the following is true? Oaifal inputs are increased by 30% then output is increased by…
