6_4(i). Consider an industry with n identical firms in which the ith firm's total cost functions is: +9n. C₁=aq+bqQ, where Q=9₁ +92 + Derive the industry's supply function.
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- Consider a manufacturing firm with total cost function: TC = 250,000 + 40Q + 0.01Q2, and market demand function: P = 940 – 0.02Q (a) Determine the firm’s profit function. (b) Determine the firm’s OPTIMAL output level. (c) Find the market price of the output at optimal operation?Given the cost information in the previous question and an industry demand function of Q = 2400 - 5p, how many firms are in this industry in the long-run equilibrium?A price-taking firm's variable cost function is C = Q3, where Q is the output per week. It has an avoidable fixed cost of $1,024 per week. Its marginal cost is MC = 3Q2. What is the profit maximizing output if the price is P = $192? 0 or 5.33 or 8 5.33 or 8 0 or 5.33 0 or 8
- The wood-pallet market contains many identical firms, each with the short-run total cost function STC(Q) = 400 + 5Q + Q2, where Q is the firm’s annual output (and all of the firm’s $400 fixed cost is sunk). The corresponding marginal cost function is SMC(Q) = 5 + 2Q. The market demand curve for this industry is D(P) = 262.5 − P/2, where P is the market price. Each firm in the industry is currently earning zero economic profit. How many firms are in this industry, and what is the market equilibrium price?Suppose a manager is faced with the following demand curve for a new software application in a monopoly market, Q = 200 - 50P and the short run total cost function is TC = 2Q + Q2 / 30 If the manager is able to maximize the firms' profit in this monopoly market, what is the total profit value?The market for drones is perfectly competitive. Assume for simplicity that fractions of everything, including firms, is possible. We have identical firms, each with a Total Cost curve of TC=376+91q+q^2 and Marginal Cost curve MC=[b]+2q. Market demand is Q=695-2P. What is the Average Total Cost if the firm produces 37 units?
- The price-demand equation for the production of bluetooth speakers is: p = 250 - 1/20x, for 0 is less than or equal to x and x is less than or equal to 5000 where x speakers can be sold at $p per each speaker. The cost to produce x speakers is given as C(x) = 150,000 + 30x, where both C(x) and p are represented in dollars ($). - find the profit function and the marginal profit and interpret the quantity P'(4500) - find the marginal cost and interpret the quantity C'(3000) - find the revenue function and the marginal revenue and interpret the quantity R'(3000)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 marginal profit function of a firm (profit (Π), point (Q) rate change depending on quantity) is MΠ = Π ^ '= dΠ / dQ = -2Q + 120. The fixed costs of the firm produced by the company are 1000 TL. In addition, the company is known to sell the goods it produces for 200 TL. Accordingly, answer the following questions.a) Find the firm's profit function.b) Find the cost function of the firm.
- Consider an HMO with a demand curve of the following form: Q = 100 – 2 P. Suppose that its marginal and average costs were $20. If the firm maximizes profits, determine its price, output, and profits.The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q + 20 + 400/q , ,where q is the firms output. Derive expressions for the firm's: (i) total cost function (ii) total profit functionConsider a computer hardware production firm with total cost function TC = 2200+480Q+20Q2, and market demand function Qd = 190 – 2P; Q is output and P is market price. (a) Determine the firm’s Total Cost when it produces 120 units of output. (b) Determine the firm’s Marginal Cost when it produces 120 units of output. (c) Determine the firm’s Average Cost when it produces 120 units of output. (d) Find the market price of the firm’s output when it sells 120 units of output. (e) Determine whether the firm makes profit, or loss, at 120 units of output.