SM 3. A firm uses capital K, labour L, and land T to produce units of...
2. A firm produces (= units of a commodity when labour input is L units. The price obtained per unit of output is P, and the price per unit of labour is w, both positive. (a) Write down the profit function w. What choice of labour input L=L* maximizes profits? (b) Consider L* as a function L (P, w) of the two prices, and define the value function (P, w) = (L* (P, w), P, w) Verify that ax/aP =...
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:
5. (a) (5 points) A firm produces aln(L 1) units of a commodity when labour input is L units The price obtained per unit is P and price per unit of labour is w, both positive, and with w<aP. Write down the profit function π. What choice of labour input L = L* maximizes profits? (5 points) Consider L* as a function of all the three parameters, L*(Ru, a), and define π"(Pu, a)= r(L', P w, a). Verify that a./...
A firm uses labour and capital to produce output according to the production function ??(??, ??) = 4??0.5??0.5, where L is the number of units of labour and K is the units of capital. The cost of labour is $40 a unit and the cost of capital is $10 a unit. a) On a graph, draw an isocost line for this firm, showing combinations of capital and labour that cost $400 and another isocost line showing combinations that cost $200....
Exercise 3 10 * K 8 If the firm uses 4 units each of labour and capital, its marginal rate of technical substitution is Based on this firm's isocost lines, if the price of capital is 2, what is the wage? 7 Answer: 6 5 4 Q = 300 Submit Answer 3 Q = 200 2 1 Q = 100 * 0 0 1 2 3 4 5 6 7 8 9 10 What labour-capital combination is the least cost...
Question 2: Firms Consider a firm that produces output Y from capital K and labour N using the production iechoolopy Y KNdThe f's capital endowcnt is piven as K 50 Labour is hired to maximize profits. At a wage rate w, the firm's labour costs are wN The firm's profit (as a function of N is therefore 1. Find the firm's labour demand function by maximizing profits and solving the fist order condition for the wage rate w. 2. Plot...
3. A firm intends to produce 30 units of output (Q) as cheaply as possible. The firm's production function depends on capital (K) and labour (L) and is given by Q VK + L. The price of K is 1 and the price of L is 20 (i) Write down the Lagrangian for this firm's optimisation problem. ii Find the optimal choices of K and L (ii) Report and interpret your solution for the Lagrange multiplier
3. A firm intends to produce 30 units of output (Q) as cheaply as possible. The firm's production function depends on capital (K) and labour (L) and is given by Q -v 20. L + K. The price of L is €1 and the price of K is i) Write down the Lagrangian for this firm's optimisation problem. (ii) Find the optimal choices of K and L ii) Report and interpret your solution for the Lagrange multiplier. 1 of 1
A firm produces output Q by using capital K and labor L in fixed proportions, i.e. Q = F (K ,L ) = min {K, L/3}. The price of a unit of labor is w = 6, the price of a unit of capital is r = 2 and the price of output is p = 20. a) Draw the isoquant for Q = 8. b) Find the marginal product of labor. Suppose that (in part c and d) the...
3. A firm intends to produce 30 units of output (Q) as cheaply as possible. The firm's production function depends on capital (K) and labour (L) and is given by Q 20 VL+K. The price ofL is 1 and the price of K is i) Write down the Lagrangian for this firm's optimisation problem. (ii) Find the optimal choices of K and L. ii) Report and interpret your solution for the Lagrange multiplier.