Production Cost Per Edition Is Tc (Q)

¶ … Production Cost Per Edition Is TC (Q) =70+0.10Q+0.001Q2 Functions (i) Total Revenue Function Total Revenue is normally calculated by multiplying the price of the product with the quantity sold. TR (Q) =P (Q) x Q. where Q. is the quantity of output sold, and P (Q) is the inverse demand function of the price.

Price per unit is Simplified function 0.90Q2 Profit Function The profit is calculated by subtracting the production cost from the total revenue (Q) = TR (Q) - TC (Q) Production cost =70+0.10Q+0.001Q2 P (Q) x Q -- (70+0.10Q+0.001Q2) where P. Or ? is the price per Unit PQ2-70+0.10Q+0.001Q2 Price per copy is Q2 -70+0.10Q+0.001Q2 Profit Function = 0.9010 Q2 +0.10Q -70 Marginal Revenue Function The marginal revenue is the extra revenue that comes from selling 1 additional unit.

The change in revenue with respect to a change in quantity must be computed first. MR (Q)= d (TR) Where'd represent derivative dQ Total Revenue function = 0.90Q2 MR (Q)= d (TR) =d (0.90Q2) dQ d (Q) Marginal cost Function The marginal unit is the last unit. Therefore, marginal cost is the cost of the last unit, or what it costs to produce one more unit.

The change in costs from a previous level divided by the change in quantity from the previous level is represented by MC = Change in TC / Change in Q MC (Q)= d (TC) d (Q) The function is =MC (Q)=d (70+0.10Q+0.001Q2) d (Q) Marginal profit Function M ? = R ' (Q) - C ' (Q) Marginal revenue is d (0.90Q2) - d (70+0.10Q+0.001Q2) d (Q) d (Q) M ? = 0.90Q2 - (70+0.10Q+0.001Q2 ) QQ M ? = 0.90Q - (70+0.10Q+0.001Q2 ) Q Average cost function Average cost is total revenue divided by the number of quantity MC= 0.90Q2 Q Manipulate the total revenue, profit, marginal revenue, marginal cost, marginal profit and average cost given that Q=500 Total revenue TR (Q) =P (Q) x Q= 0.90Q2 0.90 x 5002 =0.90 x 250000 TR=225000 (i) Profit Profit function is 0.9010 Q2 +0.10Q -70 Q=500 (0.9010 x 5002 ) + (0.10 x 500) -- 70 225250 + 50-70 P =225230 (ii) Marginal Revenue Marginal revenue function is MR (Q) = d (TR) =d (0.90Q2) dQ d (Q) Q=500 =d (0.90Q2) d (Q) 500 = 0.90 x 250000 = 450 MR = 450 (iii) Marginal cost The MC function is d (70+0.10Q+0.001Q2) d (Q) Q=500 d (70+0.10Q+0.001Q2) d (Q) = 70+0.10Q+0.001Q2 Q 70+ (0.10 x 500) + (0.001 x 5002 ) = 70+50 +250 MC = 370 (iv) Marginal profit The marginal profit function is M ? = 0.90Q - (70+0.10Q+0.001Q2) Q Q= 500 Therefore, M ? is (0.90 x 500) - 70+ (0.10 x 500) + (0.001 x 5002 ) =450-70 + 50 +250 M ? = 450-370/500 = 449.26 (v) The average cost Average cost function is MC= 0.90Q2 Q 0.90 x 5002 = 225000/500 = 450 (b) Profit maximization Since marginal cost of $370 is less than marginal revenue of $450, the newspaper sales should be increased to optimize profit until marginal cost equals marginal revenue.

(c) Graph of MR and MC The point of intersection is 300 The intersection point of MR and MC meet is 300. When the industry is perfectly competitive, the manufacturing company should face a demand curve that is identical to its marginal revenue curve (MR).Accordingly, the marginal revenue curve would have a negative gradient, due to the overall market demand curve. (d) The production level that would make it necessary to stop producing newspaper.

When the total cost of production (TC) appears to be greater than the Total Revenue (TR), losses are realized without delay. This kind of sale creates a realized and recognized loss at the same time immediately after the sales. At this point, it would be necessary to stop the production of newspapers because the main purpose of business is to pay back the production expenses incurred and make profit at the same time. 2.

Manufacturing cost of an Item is TC (Q) =6000+5Q+ Q2 / 60 (a) Average cost Q is 1 TC = 6000+ (5 x 1) + (12/60) TC = 6000 + 5 + 0.02 TC= 6005.02 Average cost = TC/Q 6005.02/1 AC= 6005.02 b) Average cost.