10. Suppose there are 1000 identical rms producing heads oflettuce in a perfectly competitive market and that the total cost curve for each rm is given by TC=q2 + 4:; + 20 and MC = q+4. a. Write an equation for the typical firm's shortrun supply curve? b. Graph the firm's short run supply curve: Firm Market 20 2D 19 19 lg 18 15 16 15 15 14 14 13 12 11 c,11 110 310 \"'9 9 S S 7 7' 6 6 5 5 4 3 3 AVG 2 1 2 o 1 nnnnnnnnnnnnnnnn D oawmqmmhmmgmg Hqummhmmgg q of heads ofle'rtuce 0. of heads of lettuce c. Derive and graph the market short-run supply curve. That is, solve the rm's supply curve for q and add it up! d. Graph the market supply curve. Double check that it is consistent with 1000 ofthe rm supply curves that you drew in the left hand side rm graph. e. Ifthe market inverse demand curve is P = 10 $09, what are P* and Q\" in the short-run? Show the algebra and graph this. f. How many heads oflettuce is each lettuce farm producing? Show your algebraic work using the prot maximizing rulell g. Graph the demand curve for the lettuce farm. Label it \"\"d h. What are the prots in this market? Calculate each rm's prots, and then multiply it by the number of rms. Are they sustainable in the long run? i. Graphically illustrate the consumer and producer surplus at the market equilibrium. Label them CS and PS. j. Suppose Imani decides to buy out all 1000 lettuce 20 firms at once and monopolize the lettuce market. i; Assume she successfully buys everyone's firm and i; that there are no cost advantages associated with 15 being a monopolist (her costs don't change when she becomes a monopoly). Also assume the demand is if the same whether the market is perfectly competitive g lg or monopolistic. Graph the demand and MC 3 curve for Imani's company. (Hint: Imani wants 2 the MC to be equal for all her 1000 plantsf'lettuce E producing locations, so she will add up the MC,just 3 like you did in the perfect competition case above, 1 - 0 however, P does not equal MC in a monopoly.) C, C, C, C, C, C, c, c, c, c, c, c, c, c, c, 0 888888888888888 -l N m \"3' Ln LE) I"'- [III 0') (:3 H N m \"3' Ln Il Il Il Il Il Il Q of heads of lettuce i. What is the monopoly's profit maximizing quantity and price? Hint: What is Imani's MR? To maximize profit as a monopolist set MC = MR. j. How many heads oflettuce are produced by each farm (lettuce producing location) within the giant firm? k. How profitable is each plant? Based on that number, what are Imani's profits as the monopolist? Are these sustainable in the long run? 1. Graphically illustrate the producer and consumer surplus and any inefficiency. m. Do you believe costs wouldn't change if the many firms are merged into a single firm? Use returns to scale in your answer. Would there be increasing, decreasing or constant returns to scale if 1000 lettuce producing firms merged into one? Defend your answer and discuss how it will affect costs