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![-PCKL)- KOLO 63/516 Long Run problem. Min Whatok st q = 4315 [15 L = whtok tar ā- k315 [15 ] FOC: ah = w- K31E 415 ao al L1](http://img.homeworklib.com/questions/bea1e480-0754-11ea-8d33-831d7ec14d4e.png?x-oss-process=image/resize,w_560)
![then P = § 9 14 2314 w/4 [ (37314 + 3/4] q= r 4P [ 5A (8)314 wl 1er CP,wo) = [Les too. w. Ang then (*= q*514 633/4 (W) YA A.](http://img.homeworklib.com/questions/bf5edfa0-0754-11ea-9790-15f727d624d2.png?x-oss-process=image/resize,w_560)
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5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,r,q) and labor L*(w,r,q), and the long run minimized cost C* (w,r,q). (Hint: reduce the cost function for the next part. (b) Setup and solve the profit maximization problem over quantity using the cost function you solved for in the previous part. Solve for the profit maximizing quantity q *(p,w,r), cost...
4. Production of bikes requires 3 workers for every 2 machines, such that bikes are prodaced...
4. Production of bikes requires 3 workers for every 2 machines, such that bikes are prodaced according to F(K.L) min(3K, 2L) (a) Setup the short run cost minimization problem when R-6. (2 points) 5 (b) Solve for the short run optimal amount of labor Lsle) and short run minimized cost Csa(w,r.q). (3 points) (e) Now suppose the bike shop can freely choose capita! (K) and labor (L). Setup the long run cost minimiza- tion problem. (2 points) (d) Solve for...
4. Production of bikes requires 3 workens for every 2 machines, such that bikes are produced...
4. Production of bikes requires 3 workens for every 2 machines, such that bikes are produced according to F(K.L)-min 3K.2) (a) Setup the short run cost minimization problem when &6 (2 points) 5 (b) Solve for the short run optimal amount of labor Lsar(g) and short nun minimized cost Csr(wrg). (3 points) (e) Now suppose the bike shop can freely choose capital (K) and labor L Setup the long rn cost minimira tion problem. (2 points) (d) Solve for the...
1. Consider the profit maximization problem for the firm. Say the pro- duction function f(k, n)...
1. Consider the profit maximization problem for the firm. Say the pro- duction function f(k, n) is strictly concave jointly in all arguments and once continuously differentiable (C), where k (resp, n) denotes the input of capital (resp, labor) (a) Assume a maximum exists for the firms profit maximization problem. What are the first order conditions (FOCs) to characterize all optimal solutions for factor demands for capital and labor in the general problem? (b) Say f(k, n) = (ak" +...
1. Consider a flower shop that uses sunflowers (s) and daisies (d) to produce bouquets. The...
1. Consider a flower shop that uses sunflowers (s) and daisies (d) to produce bouquets. The cost for a sunflower is p, and the cost for a daisy is pd. The quantity of bouquets is g. The flower shop sees these flowers as perfect substitutes such that bouquets are produced as: F(s.d) = 2s +50 (a) Suppose the delivery of sunflowers is delayed and are stuck with a certain number of sunflowers. In particular, they have 5 = 10 sunflowers....
1. Suppose cars are produced using workers and machines as perfect complements. The production func- tion...
1. Suppose cars are produced using workers and machines as perfect complements. The production func- tion for producing cars is: F(K, L) = min(2K,5L) (a) Setup the short run cost minimization problem when K = 10. (2 points) (b) Solve for the short run optimal amount of labor Lsr() and short run minimized cost Csr(w,r,q). Circle your answer. (4 points) (c) Now suppose the car factory can freely choose capital (K) and labor (L). Setup the long run cost minimization...
3. Consider a flower shop that uses sunflowers (s) and daisies (d) to produce bouquets. The...
3. Consider a flower shop that uses sunflowers (s) and daisies (d) to produce bouquets. The cost for a sunflower is Ps and the cost for a daisy is pd. The quantity of bouquets is q. The flower shop sees these flowers as perfect substitutes such that bouquets are produced as: F(s,d) 4s+2d (a) Suppose the delivery of sunflowers is delayed and are stuck with a certain number of sunflowers. In particular, they have s 40 sunflowers. Setup the short...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
Question 4 Consider the production process with 2 inputs and 1 output. The production function is...
Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y The input prices are w and w2 respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) 1/3 1/3 (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w, and output price...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
4. Production of bikes requires 3 workers for every 2 machines, such that bikes are prodaced according to F(K.L) min(3K, 2L) (a) Setup the short run cost minimization problem when R-6. (2 points) 5 (b) Solve for the short run optimal amount of labor Lsle) and short run minimized cost Csa(w,r.q). (3 points) (e) Now suppose the bike shop can freely choose capita! (K) and labor (L). Setup the long run cost minimiza- tion problem. (2 points) (d) Solve for...
4. Production of bikes requires 3 workens for every 2 machines, such that bikes are produced according to F(K.L)-min 3K.2) (a) Setup the short run cost minimization problem when &6 (2 points) 5 (b) Solve for the short run optimal amount of labor Lsar(g) and short nun minimized cost Csr(wrg). (3 points) (e) Now suppose the bike shop can freely choose capital (K) and labor L Setup the long rn cost minimira tion problem. (2 points) (d) Solve for the...
1. Consider the profit maximization problem for the firm. Say the pro- duction function f(k, n) is strictly concave jointly in all arguments and once continuously differentiable (C), where k (resp, n) denotes the input of capital (resp, labor) (a) Assume a maximum exists for the firms profit maximization problem. What are the first order conditions (FOCs) to characterize all optimal solutions for factor demands for capital and labor in the general problem? (b) Say f(k, n) = (ak" +...
1. Consider a flower shop that uses sunflowers (s) and daisies (d) to produce bouquets. The cost for a sunflower is p, and the cost for a daisy is pd. The quantity of bouquets is g. The flower shop sees these flowers as perfect substitutes such that bouquets are produced as: F(s.d) = 2s +50 (a) Suppose the delivery of sunflowers is delayed and are stuck with a certain number of sunflowers. In particular, they have 5 = 10 sunflowers....
1. Suppose cars are produced using workers and machines as perfect complements. The production func- tion for producing cars is: F(K, L) = min(2K,5L) (a) Setup the short run cost minimization problem when K = 10. (2 points) (b) Solve for the short run optimal amount of labor Lsr() and short run minimized cost Csr(w,r,q). Circle your answer. (4 points) (c) Now suppose the car factory can freely choose capital (K) and labor (L). Setup the long run cost minimization...
3. Consider a flower shop that uses sunflowers (s) and daisies (d) to produce bouquets. The cost for a sunflower is Ps and the cost for a daisy is pd. The quantity of bouquets is q. The flower shop sees these flowers as perfect substitutes such that bouquets are produced as: F(s,d) 4s+2d (a) Suppose the delivery of sunflowers is delayed and are stuck with a certain number of sunflowers. In particular, they have s 40 sunflowers. Setup the short...
Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y The input prices are w and w2 respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) 1/3 1/3 (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w, and output price...
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