1 / 7

Marginal Analysis

Marginal Analysis. Rules. Marginal cost is the rate at which the total cost is changing, so it is the gradient, or the differentiation. Total Cost, TC = y, then Marginal Cost, MC = dy / dx .

zeroun
Download Presentation

Marginal Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Marginal Analysis

  2. Rules • Marginal cost is the rate at which the total cost is changing, so it is the gradient, or the differentiation. • Total Cost, TC = y, then Marginal Cost, MC = dy/dx. • Marginal Revenue is the rate at which the total revenue is changing, or the gradient or differentiation. • Total Revenue, TR = y, then Marginal Revenue, MR = dy/dx. • Total Profit, TP = TR - TC

  3. Example(1) • The total cost of making x units of a product is TC=2X2+4X+500. What are: • The fixed cost? • The variable cost? • The marginal cost? • The average cost? • What are the costs of making 500 units of the product?

  4. Solution • Total Cost, TC=2X2+4X+500. • Fixed Cost = 500 , not effected by the quantity. • Variable Cost = 2X2 + 4X, changed by quantity. • Marginal Cost MC = dy/dx = 4X + 4 • Average Cost = TC/X = 2X + 4 + 500/X • When x = 500: TC = 502,500 FC = 500 VC = 502,000 MC = 2,004 AC = 1,005

  5. Example(2) • The total revenue and total cost for a product are related to production x by: • TR = 14X – X2 + 2000 • TC = X3 -15X2 + 1000 • How many units should the company make to: • Maximise total revenue • Minimise total cost • Maximise profit

  6. Solution • MR = dy/dx for TR = 14 – 2X, the turning point occurs when MR = 0, so, 14 – 2X = 0 gives X = 7. d2y/dx2 = -2 < 0 , turning point is maximum, when X = 7, TR = 2,049. • MC = dy/dx for TC = 3X2 – 30X, the turning point occurs when MC = 0, so, 3X2 – 30X = 0; when X = 0 or X = 10. d2y/dx2 = 6X – 30, when X=0, d2y/dx2 = -30 < 0 (maximum), when X = 10, d2y/dx2 > 0, (minimum) Then, when X=10, TC = 500.

  7. Solution (Continued) • TP = TR – TC = -X3 + 14X2 + 14x + 1000, dy/dx = -3X2 + 28X + 14 • Use the quadratic equation, the positive root is 9.8 . • d2y/dx2 = -6X + 28, When X = 9.8, d2y/dx2 < 0, confirming a maximum. At this point, the maximum profit = 1540.6

More Related