The long-run cost function of the representative firm in an industry is C(q)=q3/3-6q2 +30q and the market demand function is D(p)=3600-120p. Determine the quantity supplied by the representative firm, the market price, the total sales, and the number of firms in the long-run industry equilibrium.
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The long-run cost function of the representative firm in an industry is C(q)=q3/3-6q2 +30q and the
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- Multiplying one firm’s short-run supply function to the number of firms in a specified industry will give you the short-run market supply function. True or false.A competitive industry consists of 100 identical firms. The short run cost function of each firm is given by C(q)=200q+15q^2 What is the supply function for each firm?A competitive industry consists of 100 identical firms. The short run cost function of each firm is given by C(q)=200q+15q^2 What is the market supply function?
- 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 firm operating in a perfectly competitive industry has costs in the short run given by: SRTC = 8 + ½q^2 and therefore MC = q. Assuming that the firm is a price-taker operating in a competitive market, derive an expression for the firm’s supply curve, (the profit maximizing output for the firm as a function of the market price, i.e., q^s = f(p). Assuming the firm is one of 100 identical firms in the industry, what is the short-run supply curve for the industry, i.e., Q^s = f(p)? If demand is given by Q^D = 1000 – 100p, what are the short-run equilibrium price, market quantity, and firm quantity? Is this a long-run equilibrium? [Hint: Calculate firm profit in the equilibrium.]. Suppose a firm operating in a perfectly competitive industry has costs in the short run given by: SRTC = 8 + ½q2 and therefore MC = q. Assuming that the firm is a price-taker operating in a competitive market, derive an expression for the firm’s supply curve, (the profit maximizing output for the firm as a function of the market price, i.e., q S = f(p). Assuming the firm is one of 100 identical firms in the industry, what is the short-run supply curve for the industry, i.e., Q S = f(p)? If demand is given by Q D = 1000 – 100p, what are the short-run equilibrium price, market quantity, and firm quantity? Is this a long-run equilibrium? [Hint: Calculate firm profit in the equilibrium.]
- A perfectly competitive industry has a large number of potential entrants. Each firm has an identical cost structure such that long-run average cost is minimized at an output of 20 units (qi) =20. The minimum average cost is $10 per unit. Total market demand is given by ? = 1,500 − 50? Calculate the short-run supply function for each firm and the industry short-run supply function.A firm produces a product in a competitive industry and has a total cost function C = 80 + 4q + 2q2 and a marginal cost function MC = 4 + 4q. At the given market price of $28, the firm is producing 7 units of output. Is the firm maximizing its profit? What quantity of output should the firm produce in the long run?Suppose that many small firms operating in the perfectly competitive market set-up. All firms are identical and have the total cost function c (q)= 40+8q+(q^2/10), where q is the individual firm’s production amount. The market inverse demand function is described as P= A - (Q/50), where A>0 is constant, and Q is the market quantity. In the short-run equilibrium, there are 78 firms in the market, and firm’s maximum profit is $22.5 a) find the short-run equilibrium price b) suppose that in the long-run, firms cost function is still the same C (q)= 40+8q+(q^2/10) (assume LR cost function has fixed component of 40) Find the long-run equilibrium number of firms? (Assume market demand in LR = market demand SR)
- Which of the following statements is correct? *In order to maximize profits in the short run, a purely competitive firm should produce at the level where marginal cost is equal to price. A purely competitive firm will produce in the short run, so long as total receipts are sufficient to cover its total fixed costs. A purely competitive firm will always close down in the short run, whenever price is less than average total cost. In the long-run, firms incur costs that are fixed and variable.Consider a competitive industry with a market demand curve of P = 120 - Q, where P is market price and Q is the quantity demanded in the market. In the short run there are 4 firms in the industry, and each firm has a total cost function of TC = 144 + q^2, where q is output of the individual firm. The short-run industry supply curve Qs is?Assuming fixed costs are unavoidable in the short run, a perfectly competitive firm’s short run supply curve is the portion of Group of answer choices a) its MC curve that lies above its average total cost curve. b) its average variable cost curve that lies below its average total cost curve. c) its MC curve that lies above its average variable cost curve. d) its average variable cost curve that lies above its average total cost curve.
