Let AC(q) and MC(q) be the average cost function and the marginal cost function respectively. (a) Show that if AC(q) has a critical point at q = q*, then MC(q*) AC(q*). (b) Use the second derivative test to write down the conditions (in terms of MC(q)) for the average cost function AC(q) being minimized at q = q*.
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- Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when x = a. c. Interpret the values obtained in part (b). C(x) = 0.04x³ +0.4x² + 30x+130, 0≤x≤ 1500, a = 1000 a. The average cost function is C(x)=Introduction to Calculus in Economics: Calculus is a powerful tool used in economics. One of the initial applications areas is the study of a firm, a topic in microeconomics. An important function is the cost function function C(x), the cost of producing items (of whatever they are selling). This question deals with just the cost function C'(x). Problem Set question: The cost, in dollars, of producing a units of a certain item is given by C(x) = 10x10√x - 8. Find the production level that minimizes the average cost per unit. The number of units that minimizes the average cost is NumberIntroduction to Calculus in Economics: Calculus is a powerful tool used in economics. One of the initial applications areas is the study of a firm, a topic in microeconomics. An important function is the cost function function C (z), the cost of producing z items (of whatever they are selling). This question deals with just the cost function C (z). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (z) = 5z – 8/I – 3. Find the production level that minimizes the average cost per unit. The number of units that minimizes the average cost is Number
- Consider the following cost function: C(q) = 100 + 10q+q² (i) What are the formulas for the Total Fixed Cost (TFC), Total Variable Cost (TVC), Average Total Cost (ATC) and Marginal Cost? (ii) At what output level is Average Total Cost (ATC) lowest? What is the minimum Average Total Cost (ATC)? (iii)4. Variouss measures of cost Douglas Fur is a small manufacturer of fake-fur boots in San Diego. The following table shows the company's total cost of production at various production quantities. Fill in the remaining cells of the following table. Quantity Total Cost Marginal Cost (Dollars) Fixed Cost Variable Cost Average Variable Cost Average Total Cost (Pairs) (Dollars) (Dollars) (Dollars) (Dollars per pair) (Dollars per pair) 120 1 200 2 240 3 285 4 340 425 6 540 On the following graph, plot Douglas Fur's average total cost (ATC) curve using the green points (triangle symbol). Next, plot its average variable cost (AVC) curve using the purple points (diamond symbol). Finally, plot its marginal cost (MC) curve using the orange points (square symbol). (Hint: For ATC and AVC, plot the points on the integer; for example, the ATC of producing one pair of boots is $200, so you should start your ATC curve by placing a green point at (1, 200). For MC, plot the points between the integers:…Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when x=a. c. Interpret the values obtained in part (b). C(x)=0.04x^3+0.6x^2+60x+120, 0≤x≤1500, a=800
- Is this right or wrong (The question is the screenshot) (A) We want to minimize the cost function C(x, y) = 9x + 12y subject to the constraint U(x, y) =x (y + 3) = 128.9 and non-negativity constraints × ≥ 0 and y ≥ 0 We set up the Lagrangian: L(x, y, λ) = C(x, y) - λ(U(x, y) - 128.9) Now, we calculate the partial derivatives with respect to x, y, and 1: ∂L/∂x = 9 - λ(y + 3) ∂L/∂y = 12 - λX ∂L/λ = 128.9 - U(x, y) Setting these partial derivatives equal to zero, we have: 9 - λ(y + 3) = 0 2 12 - λx = 0 128.9 - x(y + 3) = 0 From equation 2, we get λ= 12/x. Substituting A into equations 1 and 3: 9 - (12/x)(y + 3) = 0 2. 128.9 - xY - 3x = 0 Now, we can solve this system of equations simultaneously. Let's start by solving equation 2 for X: 128.9 - xy - 3x = 0 xy = 128.9 - 3x Now, substitute this into equation 1: 9 - (12/x)(y + 3) = 0 9-(12/x)(128.9 - 3x + 3) = 0 9- (12/x)(131.9 -3x) = 0 9 -1,582.8/x + 36x = 0 Multiply through by x to get rid of the fraction: 9x - 1.582.8 ÷…Let C(T) be a function that models the dependence of the cost (C) in thousands of dollars on the amount of ore to extract from a copper mine measured in tons (T): 1) If you computed the average rate of change of cost with respect to tons for production levels between T = 20000 and T = 40000, give the units of your answer (no calculations - describe the units of the rate of change). 2) If you had a function for C(T) and were able to calculate the answer to part 1, explain why you would not expect your answer to be negative (explanation should be in terms of cost, tons of ore to extract, and rates of change).The weekly cost C of producing x units in a manufacturing process is given by C(x) = 60x + 2250. The number of units x produced in t hours is given by x(t) = 50t. (a) Find and interpret (C ∘ x)(t). (C ∘ x)(t) = (C∘x)(t) represents the cost of production as a function of time. (C∘x)(t) represents the production as a function of cost. (b) Find the cost of the units produced in 4 hours.$ (c) Find the time that must elapse in order for the cost to increase to $15,000. hr
- The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2,600x – 0.06x2. (a) Find the marginal cost function C'(x). C'(x) = (b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars. The cost to air the 5th commercial is approximately X dollars. (c) What is the exact cost to air the 5th commercial? Convert your answer to dollars. The exact cost to air the 5th commercial is x dollars.1. For each of the cost functions given below, do the following things: C(T) = = 10 + 2T. C(T) = T0.8 (a) Draw the graph for C(T), with T on the horizontal axis. Explicitly the values for the intercepts. (b) Derive AC and MC respectively, and draw their curves. (c) Determine whether the cost function exhibits IRTS or DRTS or CRTS.A company manufactures mountain bikes. The research department produced the marginal cost function C'(x)=500-3, 0≤x≤ 900, where C'(x) is in dollars and x is the number of bikes produced per month. Compute the increase in cost going from a production level of 450 bikes per month to 600 bikes per month. Set up a definite integral and evaluate it. ← The increase in cost is $