Let the production function be Q = (K0.5 +L0.5)2 and assume that both factors are variable. (a) Derive the contingent...
Let the production function be Q = (K0.5 +L0.5)2 and assume that both factors are variable.
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(a) Derive the contingent demand functions for K and L
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(b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function.
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(c) Find the amount of K and L necessary to produce Q = 200 when v = 8 and w = 2.
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(d) For general w, v and Q, find the average and marginal cost functions.
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Let the production function be Q = (K0.5 +L0.5)2 and assume that both factors are variable. (a) Derive the contingent...
Derive the cost function associated with the production function in questions 2 is C(q) = 4...
Derive the cost function associated with the production function
in questions 2 is C(q) = 4 + 2q and in questions 3 is
C=wL+rK=1*8+2*4=16. The cost function is of the general form C(Q) =
xQ. What is the value of x?
2. The inverse market demand function is given by P()-20 q. Would consumers prefer to face a monopolist in this market with a cost function given by C(g)4+ 2q, or a perfectly competitive firm with a cost function given...
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at...
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at 100 units. Derive and plot Page 2 of . The total product function q(L) ii. The marginal product function MPL(L) ii. The average product function AP(L) (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at 100 units. Derive and plot: i, The total product function q(L) ii. The marginal product function MPL(L). iii. The average product function APL(L). (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short run average cost....
4. Your production function is Q = LK. The wage for L is w and the...
4. Your production function is Q = LK. The wage for L is w and the rental rate for K is r. You need to produce Q units of output. (a) What is your total cost equation? (b) What is your output constraint? (c) Find the Marginal Rate of Technical Substitution (MRTS) for your production function. (d) In general (for any values of w and r), what relationship must hold between L and K at the cost minimizing bundle? (e)...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
Let the production function be as follow: 2. L0.7 K.3 q(L, K) Also assume w 2 and r=4 Find out if we have increasing...
Let the production function be as follow: 2. L0.7 K.3 q(L, K) Also assume w 2 and r=4 Find out if we have increasing, decreasing or constant return to scale. a. Derive the long-run cost function. TC(q) b. Derive the average cost curve. Is it increasing or decreasing or constant in q? С. Let the production function be as follow: 3. q(L, K) LK3 Also assume w-4 and r=3 Find out if we have increasing, decreasing or constant return to...
2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a....
2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a. For some w, y, use the Lagrangean method to derive demand functions by finding the cost-minimizing combinations of k and I in terms of q, w, and y (so the cost function is the objective function, and the production function is the constraint). (10 points) b. What is the rate of technical substitution (RTS) for this function? (5 points) C. Presume that the firm...
2. Consider a firm producing pizza with production function q = KL, that faces input prices...
2. Consider a firm producing pizza with production function q = KL, that faces input prices w= $10 and r = $100 for labor and capital, respectively. a. Derive the isoquant equation. Find the isoquant of an output q = 1. Draw it in a figure with l in the horizontal axis and k in the vertical axis. b. Does this firm's production exhibit increasing, decreasing or constant returns to scale? Briefly explain c. Find the labor demand, and the...
1) (Cost functions) a) Consider total cost function: C(q) = 48 + 3q2 + 2q, derive...
1) (Cost functions) a) Consider total cost function: C(q) = 48 + 3q2 + 2q, derive the average cost function, the marginal cost function, and the minimum efficient scale, and carefully graph the average cost and marginal cost curves. b) Consider total cost function: C(q) = 20 + 5q, derive the average cost function, the marginal cost function. How does the marginal cost compare to the average cost? Graph these two functions. Does the average cost obtain a minimum at...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):=...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
Derive the cost function associated with the production function
in questions 2 is C(q) = 4 + 2q and in questions 3 is
C=wL+rK=1*8+2*4=16. The cost function is of the general form C(Q) =
xQ. What is the value of x?
2. The inverse market demand function is given by P()-20 q. Would consumers prefer to face a monopolist in this market with a cost function given by C(g)4+ 2q, or a perfectly competitive firm with a cost function given...
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at 100 units. Derive and plot Page 2 of . The total product function q(L) ii. The marginal product function MPL(L) ii. The average product function AP(L) (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at 100 units. Derive and plot: i, The total product function q(L) ii. The marginal product function MPL(L). iii. The average product function APL(L). (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short run average cost....
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
Let the production function be as follow: 2. L0.7 K.3 q(L, K) Also assume w 2 and r=4 Find out if we have increasing, decreasing or constant return to scale. a. Derive the long-run cost function. TC(q) b. Derive the average cost curve. Is it increasing or decreasing or constant in q? С. Let the production function be as follow: 3. q(L, K) LK3 Also assume w-4 and r=3 Find out if we have increasing, decreasing or constant return to...
2. Marginal products, RTS, and elasticity of substitution: Consider the following production function: q=k *11/4 a. For some w, y, use the Lagrangean method to derive demand functions by finding the cost-minimizing combinations of k and I in terms of q, w, and y (so the cost function is the objective function, and the production function is the constraint). (10 points) b. What is the rate of technical substitution (RTS) for this function? (5 points) C. Presume that the firm...
2. Consider a firm producing pizza with production function q = KL, that faces input prices w= $10 and r = $100 for labor and capital, respectively. a. Derive the isoquant equation. Find the isoquant of an output q = 1. Draw it in a figure with l in the horizontal axis and k in the vertical axis. b. Does this firm's production exhibit increasing, decreasing or constant returns to scale? Briefly explain c. Find the labor demand, and the...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
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