Minimization CT = W1X1 + W2X2 Hold it: Y = X11/3 X21/6 where X1 and X2 are the productive factors and W1 and W2 are their prices, respectively. Determine: If X2 = 27 and W2 = 2 a) The short-run cost function
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Minimization CT = W1X1 + W2X2
Hold it: Y = X11/3 X21/6
where X1 and X2 are the productive factors and W1 and W2 are their prices, respectively.
Determine:
If X2 = 27 and W2 = 2
a) The short-run cost function
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Solved in 2 steps
- For the total cost in function: TC=15Q-8Q2+Q3, what is the output level (Q) when producing at minimum average total cost? a) 8 b) 4 c) 1 d) none of the aboveThe chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: Dependent Variable AVC R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS 19 0.7360 39.428 0.0001 PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE VARIABLE INTERCEPT 191.93 54.65 3.512 0.0029 Q -0.0305 0.00789 23.866 0.0014 Q2 0.0000024 0.00000098 2.449 0.0262 Quetsion: At what level of output will average variable cost be at a minimum? What is the minimum average variable cost?Solve correctly all the subparts Q)A firm has the following total revenue and total cost schedules: TR = $2Q. TC = $4,000 + $1.3Q. A)What is the break-even level of output? Round your answer to the nearest whole number. units What is the level of profits at sales of 6,600 units? Round your answer to the nearest dollar As the result of a major technological breakthrough, the total cost schedule is changed to: TC = $6,000 + $0.5Q. What is the break-even level of output? Round your answer to the nearest whole number. units
- Let the production function be given by q=2(square root of L)(square root of K)} and Price of K be 8 and the Price of L be 2. Then to produce 20 units of output L=.......... and K=........ minimizes cost. Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a: (5,20) b: (20,5) c: (10,10) d: (4,25) e: None of the abovef(k,l) = 1/3k1/3, the A firm is faced with a production technology that uses capital and labor: q = price of labor is w, and the price of capital is r. (a) Write down the cost minimization problem and determine the contingent input demand functions: 1(w, r, q) and k°(w, r, q). Also, derive the cost function C(w, r,q). (b) The firm operates in a perfectly-competitive market and faces a market price of p. Write down the firm's profit function. Solve the maximization problem to determine (1) input demand, that is, the demand for labor and capital as a function of w, r, and p (2) the output supply function, q as a function of w, r, and p.1. Minimize the costs for a firm faced with the cost function C = 3x² + 2xy +5y² +500 subject to the production quota x + y = 36. Show that the costs are minimized. (a) Set up the Lagrangian objective function (b) FOCs to get the critical values and stationary value (c) SOCs to verify that C* is a minimum (using a bordered Hessian matrix).
- BJO Ⓒ4 f(X₁, X₂) = (x₁² + X₂²) & 0Assume that the operation has the cost function CIC) = 200 - 30 - 80 40° and the marginal cost function MC (C) = 3- 160 - 1202. Determine the following: Average fixed cost to product 6 units of output. Average variable cost to produce 6 untis of output. Marginal cost to produce 6 units of outout Average total cost to produce 6 units of output(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.For the given cost function C(x)=250√x+ x^2/3375 -finda) The cost at the production level 1100 (ANSWERED, 8650.079) b) The average cost at the production level 1100 (ANSWERED, 7.86) c) The marginal cost at the production level 1100 (ANSWERED, 4.42) Since I have the answers for the three subparts above, how would I answer the two subparts: d) The production level that will minimize the average cost. e) The minimal average cost.Assume that housing output is a function of the quantities of capital (k) and land (l) employed by adeveloper, y = h(l, k), where h( ) is the housing production function. Also, assume that the developer’slong-run cost function is c = rl + ik, where r = price for a unit of land and i = price for a unit of capital.(a) Draw an arbitrary cost-minimizing scenario for this developer using isoquants and iso-costlines. Identify the cost-minimizing bundle as (l*, k*). Be sure to plot k along the y-axis. Pleaselabel your graphs. 5pt(b) Within a city, the price of capital, i, does not typically vary with a development’s distance fromthe city center. However, the price of land traditionally declines as distance from the centerrises. Using the cost-minimizing framework set up above, show how homes’ capital-to-landratios likely change as distance to the city center rises, holding housing output fixed. 5pt(c) Does your answer from above do anything to explain the differences in the types of homes…Given the following cost function:TC = 1500 + 15Q – 6Q2 + Q3i. Determine the total fixed cost for producing 1000 units of output and 500 units of output.ii. What is AFC at:a) 1000 units of outputb) 500 units of outputiii. Determine TVC, AVC, MC and AC at 50 units of output.SEE MORE QUESTIONS
