For the manufacturing company in problem 1, let the prices of input1 and 2 be w₁ = 10 and w₂ = 40, respectively.(A) Find the amount of each input to hire to minimize the cost ofproducing y = 100 units of output:min C (x1, x2) = 10x1 +40x2 subject to: 10x12x1/2 = 100 What is the corresponding (minimized) cost of producing these 100 units?③Ⓑ Find the input-demand functions x₁ (y) and x2(y), namely theformulas for the amount of each input that minimize the cost of producinga generic volume y of output:min C(x1, x2) = 10x1 +40x2 subject to: 10x12x3½-½ = yWhat is the corresponding (minimized) cost function, c(y)?(c)cirte) Draw the curves for the average cost, AC(y)marginal cost, MC(y) = c'(y).c(y)=and they

We got a cost minimization problem with constraint output level. Let's write the problem as Taking…

Answered: For the manufacturing company in…

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter7: Proudction Costs

Section: Chapter Questions

Problem 2SQ

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Suppose that the cost function for a commodity is C(x) = 90 + x? dollars. (a) Find the marginal cost at x = 7 units. MC(7) = [ Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 8th unit is predicted to be $ (b) Calculate C(8) - C(7) to find the actual cost of producing 1 additional unit. $4
Suppose that the total cost (in dollars) for a product is given by C(x)=1300+ 160 In(2x + 1) where x is the number of units produced. (a) Find the marginal cost MC function. MC = (b) Find the marginal cost when 160 units are produced. (Round your answer to the nearest cent.) $ Interpret your result. The profit from the next unit will be approximately this amount. This is the total cost of producing 160 units. ◇ This is the total profit from producing 160 units. ○ It will cost approximately this amount to make the next unit. (c) Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function? ○ MC ≥ 0 ○ MC > 0 ○ MC ≤ 0 ○ MC = 0 ○ MC <0 Does it apply in this problem? ○ Yes Ο ΝΟ
The total revenue function for a product is given by R=655x dollars, and the total cost function for this same product is given by C=19,250+70x+x2, where C is measured in dollars. For both functions, the input x is the number of units produced and sold. a. Form the profit function for this product from the two given functions. b. What is the profit when 25 units are produced and sold? c. What is the profit when 43 units are produced and sold?
1/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?
Want every single part
A company has the following cost functions in the short run, where the production level, Q , is measured in ‘000s of units:TC = 0.5Q^3 − 2Q^2 + 5QFC = 7(i) Calculate the optimum output level for this company in the short run.(ii) Calculate the marginal cost for this company at a production level of 3000 units
0.8₁ A firm's production function is given by Q = 40K0.8L0.2 Each unit of capital costs $40 and each unit of labour costs $80. (a) Find the maximum level of output if the total input costs are $400,000. (b) Estimate the increase in production if an addtional $5,000 is made available. (c) Show that the ratio of marginal product to price is the same for both inputs. (a) Maximum output Q = (Round to the nearest integer as needed.)
a b and c please
(a) For the cost function C(w1, w2, y) = 2y²w} w, calculate the Allen elasticity of substitution between the two inputs at the cost-minimizing input point (xf(w1, w2, y), a(w1, w2, y)). (b) Consider the production function f(r, y, z) = Vry + rz+ yz. Find the scale elasticity SE at (x, y, z) = (1,2, 3), (5, 1,6), (6, 6, 6) and determine if the pro- duction function is IRTS, CRTS, or DRTS locally at each point. (c) A profit maximizing firm in the market operates where the production exhibits decreasing return to scale (DRTS). Is this market in its long-run equilibrium? Justify your answer. (d) Suppose that there are the infinite number of potential firms that produce the identical output good y under the cost function C(y) = + 3. Assume free entry and exit. Find the long-run equilibrium output price p, the amount of the output that each firm in the market produces in the long-run equilibrium, and the value of profit that each firm earns in the equilibrium.
If you were a taxi driver, the daily revenue and cost are as the following: Revenue: $250 Variable cost (gas, your labor…): $190 Mortgage payment for car: $70 License Fee: $30 For profit maximization, will you operate your taxi business today? What is the minimum daily revenue to keep the operation in the short run? What is the minimum daily revenue to keep the operation in the long run? Please show calculation formula and/or equation.
A firm has production function F(K, L) = 1/4 (K1/2 + L1/2) . The wage rate is w = 1 and the rental rate of capital is r = 3. (a) How much capital and labor should the firm employ to produce y units of output? (b) Hence find the cost of producing y units of output (the firm’s cost function). (c) Differentiate the cost function to find the marginal cost, and verify that it is equal to the value of the Lagrange multiplier
the cost to maintain inventory for the weather balloon is given by C (x)= (21500/x)+2.4x, where x is the number of balloons in inventory. find the marginal cost for adding the 101st balloon to the inventory. explain the meaning of this extra balloon in context to the scenario.

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