Consider the following production function q = K a L b. Assume that a+b>1. Assume that...

Consider the following production function q = K ^a L ^b. Assume that a+b>1. Assume that the firm takes price of labor w, price of capital r and price of the final product p as given and minimizes costs to produce a given level of output q. Find the share of labor cost in total value of the product wL/pq as a function of q, input prices, a and b (there should not be p in your function). How does wL/pq change as q increases in your function? Explain your answer intuitively for your answer.

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Rahul Sunny answered 1 year ago

Consider a firm with a production function Q(L,K) = √L + 2√K, that faces an inverse...

Consider a firm with a production function Q(L,K) = √L + 2√K, that faces an inverse demand function P (Q) = 250 - 2Q, and the labor and capital markets are also in perfect competition. A) Derive the expression for the profit function of the firm in terms of labor and capital and express the profit maximization problem the firm faces. B) Derive the first-order conditions, and use them to get the expressions for the optimal amounts of labor and...

Consider the firm with production function given by q = f ( L , K )...

Consider the firm with production function given by q = f ( L , K ) = L ^(1/4) K^(1/4). If w = r = 4, what is the change in the producer surplus when the price increases from $16 to $32? (round your answer to one decimal place if necessary)

Consider production function Q= L^3 * K^4 - L^2 (a) Determine the MRTS L,K for this...

Consider production function Q= L^3 * K^4 - L^2 (a) Determine the MRTS L,K for this production function (b) Does this production function have an uneconomic region? If so, describe the region algebraically. (Hint: your answer will be an inequality like this: K<5L)

2. Consider a firm with the following production function: Q = K 1/3 L 2/3 (a)...

2. Consider a firm with the following production function: Q = K 1/3 L 2/3 (a) Consider an output level of Q = 100. Find the expression of the isoquant for this output level. (b) Find the marginal product of labor, MPL. Is it increasing, decreasing, or constant in the units of labor, L, that the firm uses? (c) Find the marginal product of capital, MPK. Is it increasing, decreasing, or constant in the units of capital, K, that the...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l 1−α (a) Determine the relation between α and the marginal product of k and l. For what values of α is the marginal product for each input: (i) increasing, (ii) constant, and, (iii) decreasing. (b) Show that the marginal rate of technical substitution (MRTS) is equal to α 1 − α l k . For what values of α is MRTS decreasing in k?...

Consider the Solow model economic production function, Y = A * K^a * L^(1-a) Assume the...

Consider the Solow model economic production function, Y = A * K^a * L^(1-a) Assume the following initial conditions: A = 1.2 a = 0.27 K = 16 L = 112 Additionally, you know that depreciation rate is 11 % and the savings rate is 12 %. Assuming no changes in any of the parameters, besides the change in K over time, what is the long-run equilibrium level of output?

3. Consider the production function Q = K2L , where L is labor and K is...

3. Consider the production function Q = K2L , where L is labor and K is capital. a.[4] What is the Marginal Product of Capital for this production function? Is it increasing, decreasing, or constant? Briefly explain or show how you arrived at your answer. b.[4] Does this production function exhibit increasing, constant or decreasing returns to scale? Briefly explain or show how you arrived at your answer. c.[5] If the firm has capital fixed at 15 units in the...

Consider the production function Q = K2L , where L is labor and K is capital....

Consider the production function Q = K2L , where L is labor and K is capital. a.[4] What is the Marginal Product of Capital for this production function? Is it increasing, decreasing, or constant? Briefly explain or show how you arrived at your answer. b.[4] Does this production function exhibit increasing, constant or decreasing returns to scale? Briefly explain or show how you arrived at your answer. c.[5] If the firm has capital fixed at 15 units in the short...

Consider a firm with a production function of the following form:F (L, K) = L(1/4)K(1/2) 20...

Consider a firm with a production function of the following form:F (L, K) = L(1/4)K(1/2) 20 the corresponding marginal products are MPL = 1 L(−3/4)K(1/2) 4 20MPK = 1 L(1/4)K(−1/2) 2 20 The cost of a unit of labour is the wage rate w and the cost of a unit of capital is the rental rate r. The firm is free to adjust all factors of production. (19 points) a. Does this production function exhibit decreasing returns, increasing returns, or...

Consider a firm whose production is given by Q(K, L) = K^1/3L^1/3, where K and L...

Consider a firm whose production is given by Q(K, L) = K^1/3L^1/3, where K and L are, respectively, the quantities of capital and labour production inputs. Prices of capital and labour are both $1 per unit. (a) Derive and interpret the firm’s demand functions for capital and labour. (b) Derive and interpret the firm’s Long-Run Cost Function. (c) In the long-run, if the firm wished to produce 16 units of output, what quantities of capital and labour would it optimally...

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