Given a firms demand function Q-90+2P=0 and it's average cost function AC=Q²-8Q+57+2/Q. Find the level of output which maximises marginal cost
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- Suppose the (inverse) demand for a firm’s product is given by P = 10−2Q and the cost function is C(Q) = 2Q What is the profit-maximizing level of output and price for this firm?Market demand is P = 50 -2Q. Firm has cost function TC(Q) = 5 + 2Q + Q^2. Can firm function as a price taker?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. The total cost function is C(q) = 1/30q3 – 12.85q2 + 20q + 400 . The profit function is Π(q)= –1/30q3 + 0.85q2 + 20q – 400 (i) Determine the level of output for which the firm’s profit is maximized. (ii) What is the firm's maximum profit?
- Alchem (L) is the price leader in the polyglue market. All 10 other manufacturers (follower [F] firms) sell polyglue at the same price as Alchem. Alchem allows the other firms to sell as much as they wish at the established price and supplies the remainder of the demand itself. Total demand for polyglue is given by the following function (QT = QL + QF): P = 20000 - 4QT Alchem’s marginal cost function for manufacturing and selling polyglue is MCL = 5000 + 5QL The aggregate marginal cost function for the other manufacturers of polyglue is ΣMCF = 2000 + 4QF a. To maximize profits, how much polyglue should Alchem produce and what price should it charge? b. What is the total market demand for polyglue at the price established by Alchem in Part (a)? How much of total demand do the follower firms supply?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 an expression Π (q) for the firm's profit functionAlchem (L) is the price leader in the polyglue market. All 10 other manufacturers (follower [F] firms) sell polyglue at the same price as Alchem. Alchem allows the other firms to sell as much as they wish at the established price and supplies the remainder of the demand itself. Total demand for polyglue is given by the following function (Qt= QL+Qf): P= 10,000-4Qt Alchem’s marginal cost function for manufacturing and selling polyglue is MCL= 5,000+6QL and the aggreagate marginal cost function for the other manufactorers of polyglue is EMCf= 2,000+4Qf. To maximize profits, Alchem should produce units and charge a price of $ per unit. What is the total market demand for polyglue at the price established by Alchem? units. How much of total demand do the follower firms supply? units.
- 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.Determine the output level that will create zero economic profit.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. The total cost function is C(q) = 1/30q3 – 12.85q2 + 20q + 400 . The profit function is Π(q)= –1/30q3 + 0.85q2 + 20q – 400 (i) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units?
- In order to maximize profit, the firm will choose to produce where marginal revenue is equal to marginal costA firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q + 0.25Q2. Use these two functions to form the firm's profit function and then determine the level of output that yields the profit maximum. What is the level of profit at the optimum? Note: MC = 1 + 0.5QA firm’s demand function is P= 60 − 0.5Q If fixed costs are 10 and variable costs are Q + 12 per unit, find the value of output to maximize the profit.
