A Firm has a revenue and cost function: C=1600-0.5q² R=30+200q Solve for Marginal Revenue and Marginal Cost. Find output, revenue and profit at the level of output.
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- Sergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. Currently, Sergio is selling these books for $6 each. So far this year, he has produced x a. Write a linear cost function C for Sergio’s book production, in terms of x. b. Find the linear revenue function R for selling x copies of the book. Remember that P(x) = (price)x. c. Use and 1b. to determine the profit function P for selling x books. Write the formula in simplified form. d.Use your answer for 1c to determine the profit, in dollars, for selling 300 books.If a firm's marginal revenue is below its marginal cost, an increase in production will usually: a. increase profits b. leave profits unchanged c. decrease profits d. increase marginal revenueSuppose a company's revenue function is given by R(q)=−q3+400q2R(q)=-q3+400q2 and its cost function is given by C(q)=550+12qC(q)=550+12q, where qq is hundreds of units sold/produced, while R(q)R(q) and C(q)C(q) are in total dollars of revenue and cost, respectively.A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q)=MP(q)= B) How many items (in hundreds) need to be sold to maximize profits? Answer: hundred units must be sold. (Round to two decimal places.)
- The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q +20 + 400/q, where q is the firm's output. (1) Derive and expression C(q) for the firm's total cost function.Assume that a firm’s marginal revenue curve intersects the rising portion of its marginal cost curve at 500 units of output. At this output level, a profit-maximizing firm’s total cost of production is $1,000. If the price of the product is $5 per unit, the total revenue earned by the firm will be:(29. At 100 output, marginal revenue is less than marginal cost) True False 30. In relation to question number 29, producer should produce more up to 440. True False
- Let a linear cost function C(x) = 21.95 + 1400 and a linear revenue function R(x) = 20x. What is the marginal cost? What is the marginal revenue? Write the profit function P(x). What is the marginal profit?Rasiah's Garden of fruit is a firm selling fruits in a perfectly competitive market. Total fixed cost is RM50, and the wage for labour is RM5 per worker. The estimated output produced and cost are as follows: Labour Output (Kg of fruits) usage 0. 0. 8. 10 12 20 17 30 24 40 33 50 44 60 57 70 Calculate the total variable cost, average total cost, average variable cost, marginal cost, total revenue and marginal revenue. b. If Rasiah's garden of Fruits sells a kilo of fruit for RM3.50, how many Kg of fruit (output) should the firm sell in order to maximise profits, and how much profits would the firm make?Consider a firm's total profit (TP) function as follows: TP = 50Q - Q2 (Q refers to the quantity of output) The firm's maximum level of total profit equals __________ . Select one: a. $1000 b. $25 c. $625 d. $500
- A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Find the profit-maximising level of output using the profit function and calculate how much profit is made at this output level.The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) =1/30q2 − 12.85q + 20 +400/q, where q is the firms output. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? Determine the level of output for which the firms profit is maximized. What is the firm's maximum profit?Bitcom, a manufacturer of electronics, estimates the following relation between marginal cost of production and monthly output: MC= $150+ 0.005Q What does this function imply about the effect of the law of diminishing returns on Bitcom’s short-run cost function? Calculate the marginal cost of production at 1,500, 2,000, and 3,500 units of output. Assume Bitcom operates as a price taker in a competitive market. What is this firm’s profit-maximizing level of output if the market price is $175? Compute Bitcom’s short-run supply curve for its product. Provide a 100 word summary of how this can be applied to the current economy. Show Calculations and can it be done in Excel?
