1. A general form of the Cobb-Douglas production function is given by Q = AK&L³ where A, a, ß are positive constants. A. Solve for the marginal products of capital and labor. B. For what values of a and 3 will the production function exhibit diminishing marginal returns to capital and labor? C. Solve for the marginal rate of technical substitution.

.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…

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For the production function given by /2 Hab – Aa² – Bb² , dhow that the marginal rate of technical substitution between the factors depends only on the ratio b: a of the factors used.

1. a. Suppose that the production function is Q =L"*K*4, In the short-run, with capital held fixed at K - 256. a. Find the total product function. b. Find the average product of labour (AP) function. c. Find the marginal product of labour (MP) function.

Grease Tech produces oil changes. The production of oil changes reles on both capital (K) and labor (L) and is combined in the following production function F (K, L) = KILL Take the derivative of this production function with respect to capital. What is the marginal product of capital evaluated at (le. just plug in the numbers) 64 units of capital used and 16 units of labor?

With a production function like Y=zN, which of the following must be true at the optimum?    A).The marginal product of labor is smaller than real wage.    B).The marginal product of labor is bigger than real wage.   C).The representative firm makes positive profits.   D). Profits of the representative firm are zero.

The elasticity of substitution of a Cobb-Douglas production function is constant alongthe whole range of any isoquant, and is equal to 1. Can you show this property that the elasticityof substitution is equal to one everywhere? Is the elasticity of substitution for a CES (ConstantElasticity of Substitution) production function the same?Kindly explain the answer to me.

B6

The figure shows the production function of a farmer who produces grain by working certain hours each day.     Which of the following statements is correct about this production function?         a. The slope of the production function represents the marginal rate of substitution. b. The ceteris paribus assumption means that the farmer becomes more productive as he works more hours. c. A rightward movement from B along the production function implies that the farmer has better technology. d. This production function exhibits economies of scale. e. A technological improvement would shift up the production function