A firm has two factories characterized by the following total cost functions: F1(y1)=3y², F2(y2) = y² a) In which firm is the marginal production cost are lower? b) What shares of the output should be produced in firm 1 and firm 2, if the firm minimizes total production costs? c) Derive the total cost function of production for this firm.
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- A company manufactures two products, X and Y, and the joint-cost function of these products is given by c=x+4y where c is the total cost of producing v units of X and y units of Y Determine the marginal cost with respect to y when x=36 and y=16 b. The production function for a company's product is O-20, where is the output that results from /units of labor and & units of capital. The unit cost of labor and capital are $225 and $150, respectively. The company wants the total cost of puts to be $270,000 Find the number of units of capital and labor that maximize productionIf C = 0.0001Q2 + 3Q + 6000 is a total-cost function, find the marginal cost when Q = 100.To maximise profits, a competitive firm has a cost function, C(q) = 4q2 + 95 and produces 33 units in order to maximise profits. Although the price of output does not change, the firm decides to build a second factory with the cost function C(q) = 7q2 + 45. To maximise its profits, how many units should it produce in the second factory?
- A small business woman has realized that for one of her products, if the price per unit is GH¢20 she can sell 300 units a day. On the other hand, if the price per unit is reduced to GH¢13, she can sell 440 units a day. From the accounting records, her accountant has estimated the fixed cost of production as GH₵2,000 with a variable cost per unit of GH¢10. (i). Find an expression relating price and output assuming it is linear. (ii). State the total cost function, assuming it is linear. (iii) Advise the business woman on the level of production at which she will breakeven.For the cost function C(Q) = 200+3Q2+4Q3, what is the average fixed cost of producing 10 units of output? 18.31 42.12 212.61 20If the production function of a firm is P = 60kl, where the price per unit of input k is $10 and I is $5, 1. Count the units of each input so that the total cost incurred is minimum. 2. If the firm wants to produce 120 units of output, what is the minimum total cost?
- The total cost of producing the first q items is given by the formula C(q) = -2q^3 + 60q^2 + 1000 (For example, C(10) gives the cost of the first 10 items.) a.) Find the average cost of producing items 6 through 10 b.) Find the marginal cost when q = 8Consider the following cost function: C(Q)=9,300+44Q+0.025Q 2 Calculate total costs when Q=180For the cost function C(Q) = 75 + 4Q + 2Q2, the marginal cost of producing 5 units of output is:
- Given: Q = -0.0250 L3 + 1.5 L2 The 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. The total fixed cost each month is $180,000. The following results in the picture were obtained: a) Are the estimates ˆa, ˆb, and cˆ statistically significant at the 2 percent level of significance? Which is/are significant and which is/are not?b) Do the results indicate that the average variable cost curve is ∪-shaped? How do you know? c) If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost? Marginal cost? Total variable cost? Total cost? d) Answer part c, assuming that Argus produces 10,000 vacuum cleaners monthly. e) At what level of output will average variable cost be at a minimum? What is…Market research for a certain ice cream company indicates that if the price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. Therefore, at a production level of 200 cups of ice cream, the revenue generated by the company would be $130 for each additional cup of ice cream produced. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x + 25,500. (a) Find the value(s) of x at the break-even points. (b) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.An accountant for a car rental company was recently asked to report the firm's costs of producing various levels of output. The accountant knows that the most recent estimate available of the firm's cost function is C(Q) = 100 + 10Q + Q^2, where costs are measured in thousands of dollars and output is measured in thousands of hours rented. a. What is the average fixed cost of producing 2 units of output? b. What is the average variable cost of producing 2 units of output? c. What is the average total cost of producing 2 units of output? d. What is the marginal cost of producing 2 units of output? e. What is the relation between the answers to (a), (b), and (c) above? Is this a general property of average cost curves?