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A firm's production function is given by Q = 30KL. Unit capital and labour costs are...
11. (10 points) Suppose the firm's output Q is related to capital input K and labour...
11. (10 points) Suppose the firm's output Q is related to capital input K and labour input L by the production function Q=KL (a): Find dQ/dK (marginal product of capital). (b): Find dQ/dL (marginal product of labour). (c): Find d-Q/dK2 and d-Q/dL and show that they have values less than zero (diminishing returns to factor). (d): Suppose further that K and L are given by the linear functions. Find dQ/dt if K = 5 + 2t and L= 2 +...
1. There is a furniture manufacturer using labor (L) and capital (K) to produce tables. Its production function is given by q= 10L^.75 K^.40. It pays a wage of $5 per hour and rents capital at a rate...
1. There is a furniture manufacturer using labor (L) and capital
(K) to produce tables. Its production function is given by q=
10L^.75 K^.40. It pays a
wage of $5 per hour and rents capital at a rate of $15. The firm
wants to find the cost-minimizing bundle of inputs to produce
10,000 tables. Assume K is on the y-axis in what
follows.
Write out the firm’s cost function.
Calculate the firm’s isocost equation.
What is the slope of the...
6. A firm's production function is given by q 20(EV2 +K2), where q is output and...
6. A firm's production function is given by q 20(EV2 +K2), where q is output and E and K are amounts of labour and capital, respectively. If the wage rate is w $15 per hour and the price of capital is r $60 per hour, what is the firm's profit maximizing capital/labour ratio? A. K/E 20 D. K/E 4 E. K/E = 16 B. K/E 200 C. K/E 1/2
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and...
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if f-0, the two input Labour and capital are imperfect substitutes in production
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if...
4. Suppose that a firm's production function is q = 10KiL, The Marginal Products of Capital...
4. Suppose that a firm's production function is q = 10KiL, The Marginal Products of Capital and Labour are therefore as follows. The firm can rent capital (K) and hire labour (L) at competitive rates. The cost of a unit of labour is 20 and the cost of a unit of capital is 80. (a) Write down the equation for the isocost curve. 0o iad the cos minimisi q0i (c) What is the minimum total cost (C) associated with producing...
A firm operates with the production function Q = 25K0.5L0.4 and buys input K at $20...
A firm operates with the production function Q = 25K0.5L0.4 and buys input K at $20 a unit and input L at $8 a unit. To minimize the cost of producing 400 units of Q, the firm buys ?? units of L and ?? units of K. The value of Lagrange multiplier when Q=400 is ??. In this cost minimization problem, the second principal minor of Bordered Hessian is ?? If the firm wants to increase production by 2 units...
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the...
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the number of units of outputs, labor and capital. Labor cost is $2 per unit, capital cost is $1 per unit and output sells at $8 per unit. Show that the profit function is 1=16L"2 + 24K12 - 2L-K and hence find the maximum profit and the values of Land K at which it is achieved. HINT: do not forget to check the second sufficient...
A firm with the production function Q(K,L) = 2LVKL is currently utilizing 6 units of labour...
A firm with the production function Q(K,L) = 2LVKL is currently utilizing 6 units of labour and 3 units of capital. If this is the optimal input mix, and if total costs are equal to 27, what are the prices of capital and labour? 32.16).) Capital: Labour:
A firm's Cobb-Douglas production function for output x is f(l,k)= 25/5k5, where / (labour) and k (capital) 9. are v...
A firm's Cobb-Douglas production function for output x is f(l,k)= 25/5k5, where / (labour) and k (capital) 9. are variable inputs costing w (wage rate) and r (rental cost of capital) each per unit (a) Follow the two-step (indirect) method' and begin by setting up the firm's cost- minimisation problem and deriving the three first-order conditions (FOC8) (4 marks) 2(wr)2 x2 (where, to be clear, (c) The cost function derived from the FOC8 above is c(w,r,x) 3125 1 5 the...
A perfectly competitive firm's production function is Q=17LK where Q is the amount produced, L is...
A perfectly competitive firm's production function is Q=17LK where Q is the amount produced, L is the amount of labour hired and K is the amount of capital used. P is the price that the firm gets for its product. What is the marginal revenue product of labour?
11. (10 points) Suppose the firm's output Q is related to capital input K and labour input L by the production function Q=KL (a): Find dQ/dK (marginal product of capital). (b): Find dQ/dL (marginal product of labour). (c): Find d-Q/dK2 and d-Q/dL and show that they have values less than zero (diminishing returns to factor). (d): Suppose further that K and L are given by the linear functions. Find dQ/dt if K = 5 + 2t and L= 2 +...
1. There is a furniture manufacturer using labor (L) and capital
(K) to produce tables. Its production function is given by q=
10L^.75 K^.40. It pays a
wage of $5 per hour and rents capital at a rate of $15. The firm
wants to find the cost-minimizing bundle of inputs to produce
10,000 tables. Assume K is on the y-axis in what
follows.
Write out the firm’s cost function.
Calculate the firm’s isocost equation.
What is the slope of the...
6. A firm's production function is given by q 20(EV2 +K2), where q is output and E and K are amounts of labour and capital, respectively. If the wage rate is w $15 per hour and the price of capital is r $60 per hour, what is the firm's profit maximizing capital/labour ratio? A. K/E 20 D. K/E 4 E. K/E = 16 B. K/E 200 C. K/E 1/2
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if f-0, the two input Labour and capital are imperfect substitutes in production
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if...
4. Suppose that a firm's production function is q = 10KiL, The Marginal Products of Capital and Labour are therefore as follows. The firm can rent capital (K) and hire labour (L) at competitive rates. The cost of a unit of labour is 20 and the cost of a unit of capital is 80. (a) Write down the equation for the isocost curve. 0o iad the cos minimisi q0i (c) What is the minimum total cost (C) associated with producing...
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the number of units of outputs, labor and capital. Labor cost is $2 per unit, capital cost is $1 per unit and output sells at $8 per unit. Show that the profit function is 1=16L"2 + 24K12 - 2L-K and hence find the maximum profit and the values of Land K at which it is achieved. HINT: do not forget to check the second sufficient...
A firm with the production function Q(K,L) = 2LVKL is currently utilizing 6 units of labour and 3 units of capital. If this is the optimal input mix, and if total costs are equal to 27, what are the prices of capital and labour? 32.16).) Capital: Labour:
A firm's Cobb-Douglas production function for output x is f(l,k)= 25/5k5, where / (labour) and k (capital) 9. are variable inputs costing w (wage rate) and r (rental cost of capital) each per unit (a) Follow the two-step (indirect) method' and begin by setting up the firm's cost- minimisation problem and deriving the three first-order conditions (FOC8) (4 marks) 2(wr)2 x2 (where, to be clear, (c) The cost function derived from the FOC8 above is c(w,r,x) 3125 1 5 the...
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