True or False ? Why ? In the long run, Betty’s factory produces 10,000 widgets with cost-minimizing combination of 0 units of capital and 100 units of labor. The rent (cost of capital) and the wage (cost of labor) are both $40 per day. Betty’s marginal rate of technical substitution must be greater than 1 (with L on the x-axis and K on the y-axis)
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True or False ? Why ?
In the long run, Betty’s factory produces 10,000 widgets with cost-minimizing combination of 0 units of capital and 100 units of labor. The rent (cost of capital) and the wage (cost of labor) are both $40 per day. Betty’s
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- For each of the following cases, determine whether the firm should (A) Use more labor and less capital, or (B) Use more capital and less labor. 1. The marginal rate of technical substitution is 2 (i.e., the marginal product of labor is twice the marginal product of capital) and the input price ratio is 3 (i.e., a unit of labor costs three times as much as a unit of capital) 2. The marginal rate of technical substitution is 2 (i.e., the marginal product of labor is twice the marginal product of capital) and the input price ratio is 1 (i.e., a unit of labor costs the same as a unit of capital) 3. The marginal rate of technical substitution is initially equal to the input price ratio, but the firm's machines depreciate, so that the marginal product of capital decreases. 4. The marginal rate of technical substitution is initially equal to the input price ratio, but the firm successfully negotiates a lower rate of rent for their machines, so that the price of capital decreases. 5. The…Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?Suppose that a firm’s production function is q =10L0.5K0.5 (i.e. q = 10√L√K). The cost of a unit of labour is €20 and the cost of a unit of capital is €80. The firm wants to produce 80 units of output. The marginal rate of technical substitution is K/L The optimal level of labour required to produce 80 units of output is A. 16 B. 8 C. 4 D. 2
- For a decrease in the price of capital (K), construct a table AND explain the scale and substitution effects for a producer.a firm that has the following production function: √(KL^2)Where, K and L are the units of capital and labour used in the production process respectively. a)Calculate the marginal products of labour and capital. b)What is the value of marginal rate of technical substitution when 4 units of capital and 3 units of labour are used?Question 4 The firm can use two inputs, L and K. The price of L= 20 and price of K = 30. Total cost = 300. As usual in the two input graph, units of L are on the horizontal axis and K on the vertical. The slope of the isocost line is [Select] The maximum units of K that can be purchased is [Select] The maximum units of L that can be purchased is [Select] 2 pts Is the bundle of K-9 and L- 5 on the isocost line? [Select]
- Suppose that a firm’s production function is q =L0.5K0.5. This means that the marginal rate of technical substitution is K/L.The cost of a unit of labour is $20 and the cost of a unit of capital is $80. The firm wants to produce 50 units of output. If both capital and labour are variable, how many units of labour (L) and how many units of capital (K) should be hired in the long run? A. K = 25, L =100 B. K = 10, L = 100 C. K = 25, L =10 D. K = 7, L = 28Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 20 + 55. If the price of corn feed is $4 and the price of soybean feed is $5, what is the costminimizing feed combination producing P = 200?1. Juan Valdez owns a coffee farm in Colombia. His production function is: f (x1, x2) = (x1 – 1)0.25 x9-5. Assume the price of input 1 is r and the price of input 2 is w.. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm? 2. Show that the profit function is convex in (p, w). 3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x" with A > 0, a1, ¤2 > 0 and a1 + a2 0, B > 0, 0 < a < 1, and 0 + p< 1. 6. Find the profit function for the CES production function. 7. Verify Hotelling's Lemma for the CES production function with B < 1.
- A firm produces a good using two inputs, capital (K) and labour (L). For every unit of output being produced, the ratio of capital to labour must be , where is a positive parameter. Meanwhile, the total cost of production must equal $1,000. If the rental rate of capital is $20 per unit of capital, and the hourly wage is $10 per unit of labour, how much capital does the firm use for it production? a) k=100a/(2/a+1) b) k=100/a(2a+1) c) k=100/(2/a+1) d) k=100/(2a+1)A firm uses labor (L) and capital (K) to produce outputs. The following graph shows the iso-quant curves and iso-cost curves facing this firm. The iso-quant curves are the L-shaped curves. Suppose the wage rate of labor is $200 (per day) and the rental rate of capital is $100 (per day). What is the cost of producing 20 units of output (per day) when both labor and capital are variable inputs? Notice that both inputs are variable. alae-2 (3.6) -30 = 20 - 10 O 400 O 600 1000 1200 800Consider a firm that produces a single output good Y with two input goods: labor (L) and capital (K). The firm has a technology described by the production function f : R? → R+ defined by f(1, k) = Vĩ + vk, where l is the quantity of labor and k is the quantity of capital. (a) In an appropriate diagram, illustrate the map of isoquants for the firm's production function. (b) Does the firm's technology satisfy the following properties: (i) strict monotonicity (i.e., are the marginal product of labor and the marginal product of capital strictly positive), (ii) the no-free-lunch property, (iii) constant/decreasing/increasing returns to scale? (iv) 1