A perfectly competitive firm has the following input requirement set v(y)(x1, x2): ax1+ bx2 y}. If the minimum cost of production at w₁-W2=1 is equal to 6, what is y equal to? What can you say about the elasticity of substitution for this production function?
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- Consider a production function in such a form: Q= f (K,L)= 3KL Calculate the elasticity of substitution (Ϭ) for this firm.If the demand function for math self-help videos is given by 45 -0.4x, and the total cost function to manufacture the videos is given by 4x + 17, evaluate the marginal profit function at x = 10. Marginal Profit = This means that if production and sales increase by one unit, then total profit will O increase decrease by approximately dollars.Roland Umbrellas has a production function given by Q = L0.5K0.5. The wage (W) is $80 per day and the rental per unit of capital (R) is $5 per day. In the long run, how many units of capital will Roland want to buy for each unit of labor?
- Suppose the total cost function for a firm is given by C = q(v + 2/vw + w). a) Use Shephard's lemma to compute the contingent demand functions for inputs k and l. b) Use your results from part (a) to compute the underlying production function for q. c) Compute the elasticity of substitution between inputs k and l.A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1, x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount? please solve asap?A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1, x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount?
- 2. A firm has the following Cobb-Douglas production function: q = LªK!-a, where 0 < a <1 is a parameter. Suppose that in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20. (a) Derive the marginal cost of the firm (expressed in terms of a and q). (b) Derive the average variable cost of the firm (expressed in terms of a and q). (c) Derive the cost function of the firm.Sugar Enterprises manufactures high speed personal computers as its main product line. Its short run production function is given by Q = 3600K - 4.5K² where Q is the number of computers produced in a week and K pertains to the number of units of capital. c.) Compute the marginal product of the 200th unit of capital. d.) How many computers can be produced by the firm in a week if there are 200 units of capital? e.) Compute the marginal product of the 300th unit of labor. f.) How many computers can be produced by the firm in a week if there are 300 units of labor?Suppose the long-run production function for a competitive firm is f(x1,x2)= min {3x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. A: Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. B: Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? C: Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y.
- Suppose that the manager of a firm operating in a competitive market has estimated the firm's average variable cost function to be - 0.03Q + 0.00005Q² AVC = 10 – Total fixed cost is $600. a. What is the corresponding marginal cost function? b. At what output is AVC at its minimum? c. What is the minimum value for AVC?b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L and K can vary with production. Compute the input demand functions as a function of Q. (4 Points) c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. At what prices of textile will the producer shut down production. (3 Points) d Now suppose Q = 10LK. The market prices of inputs are as in subpart (b) above. Compute the input demand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn. (5 Points)A perfectly competitive rm produces output q with capital K and labor L according to the production function: q = f(K, L) = 4K 1 4L 1 4 The price of labor is w = 4, and the price of capital is r = 4. The rm has xed costs equal to 8. The current market price is 8. (d) Find cost functions T C(q), AT C(q), and MC(q), i.e. as functions of output. At what value of q does the minimum of AT C occur? (e) Find total and marginal revenue as functions of output, i.e. T R(q) and MR(q). (f) Find the prot maximizing output q ∗ and use that to nd T R(q ∗ ), T C(q ∗ ), π(q ∗ ), L(q ∗ ), and K(q ∗ ).