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Derive an expression for average total cost atc at what

Fixed cost for a firm is given by FC = 400 and variable cost is given by VC = 5q + 1⁄4q2, where q is the output level of the firm in a given period. Therefore marginal cost for the firm is given by MC = 5 + 1⁄2q (those of you who know calculus can confirm this - MC is the first derivative of VC with respect to q).

a) Derive an expression for average variable cost (AVC). Graph MC and AVC up to q = 80. Assuming that the firm is a price-taker operating in a competitive market, derive an expression for the firm's supply curve, (ie. the profit maximizing output for the firm as a function of the market price). What is the shut-down price for this firm (ie. what is the price at or below which the firm chooses to produce zero)?

b) What does the MC curve tell us about the marginal product (MP) of the firm's variable factor of production (presumably labour)?

c) Derive an expression for average total cost (ATC). At what quantity is ATC at its minimum (at what ATC level)? In your diagram, sketch ATC and confirm that it is U-shaped. [Hint: Calculate ATC when q=20 and q= 80.]

d) Assuming that there are 150 identical firms operating in this competitive industry, what is the equation of the industry supply curve? If the demand curve is given by Q = 4500 - 100P, what is the equilibrium price, market quantity?

e) Given your answers from the previous part, what is the output level of each firm? Calculate and illustrate in your diagram the profit level for the firm? Is this a long run equilibrium? Explain.

f) Assuming that the minimum point of the short run ATC curve for all firms is also the minimum point of the long rung average cost curve (LRAC) what is the long run equilibrium price? What is the long run equilibrium market quantity and quantity per firm? How many firms are there in the long run equilibrium?

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in a pure competition market producers should produce and sell where pmc why whycouldnttheypricetheir product above mc