[60 marks]According to the Competitive and Consumer Act in Australia, cartel is ILLEGAL. A cartel is a collection of firms producing the same (or very similar) product that makes an agreement to fix prices or split the market (among other things). In this question, we try to understand why. Assume that the market is currently supplied by ten identical sellers each with variable cost VC(푞)=3푞 + 1 4 푞2, and the market demand is 퐷 = 10(7 − 푝). Assume that the market demand is sufficiently high that no seller shuts down. (a) [5 marks ]Find each seller’s marginal cost curve. (b) [10 marks ]Assume that there are sufficiently many sellers so that the market can be treated as perfectly com￾petitive. Find the competitive equilibrium. (c) [15 marks ]Compute the consumer surplus and producer surplus in the competitive equilibrium. (d) [5 marks ]Now assume that all the sellers enter a “cartel”, which consists of two agreements: (a) their product is to be sold at 푝 = 5.4; (b) Every seller is to produce 1/10 of the market demand at the cartel price. (Such 1 46p=18 24⽅ > 1 ⼈ ⼉ ⼀⼀ 今 ⼀ ⼀ Ψ→@ 、⼀ ④ 2 1⼀; ⑨ ⼝1 @ 1 B ⼀ ! …d , 1 1 ⼆ 。 E 1 B P P ⼀ ( 1 . (3) ( 2110) ( 0 . - 4 ) 12,0 ) OS: 当 X4X 号= 号 Ps:北 4×(4 ±|=4 ,6 - 3 p= - 49p P =4 q =4 替代 pd 14- 4p= - 4+ 2 pP = 3 q= 2 a cartel is highly illegal for the reason we shall see shortly.) Compute each seller’s output under the cartel. Note that under a cartel, each individual seller does not optimize anymore; they simply act according the cartel agreements. (e) [15 marks ]Compute the consumer surplus and producer surplus under the cartel. Recall that producer surplus by each seller is the difference between their revenue and the variable cost. (f) [5 marks ]Explain why the sellers prefer operating under a cartel to competing with each other without legal restrictions. (Limited to 50 words.) (g) [5 marks ]Explain why the cartel is detrimental to the entire society. (Limited to 100 words.)

(a) [5 marks] Find each seller’s marginal cost curve. The marginal cost (MC) is the derivative of the variable cost (VC). Given the variable cost function VC(q) = 3q + 1/4 q^2, the marginal cost function MC(q) is the derivative of VC(q) with respect to q. Therefore, MC(q) = 3 + 1/2 q.

(b) [10 marks] Assume that there are sufficiently many sellers so that the market can be treated as perfectly competitive. Find the competitive equilibrium. In a perfectly competitive market, the equilibrium price and quantity are determined by the intersection of the market demand and supply curves. The market supply curve is the horizontal sum of all individual firms' marginal cost curves. Given that there are 10 identical firms, the market supply curve is S(p) = 10q = 30 + 5q. The market demand curve is D(p) = 10(7 - p). Setting D(p) = S(p) and solving for p gives the equilibrium price. Substituting this price into either the demand or supply equation gives the equilibrium quantity.

(c) [15 marks] Compute the consumer surplus and producer surplus in the competitive equilibrium. Consumer surplus is the area between the demand curve and the price line, up to the equilibrium quantity. Producer surplus is the area between the price line and the supply curve, up to the equilibrium quantity. These can be calculated using the formulas for the area of a triangle and a trapezoid, respectively.

(d) [5 marks] Now assume that all the sellers enter a “cartel”, which consists of two agreements: (a) their product is to be sold at p = 5.4; (b) Every seller is to produce 1/10 of the market demand at the cartel price. Compute each seller’s output under the cartel. The market demand at the cartel price is D(5.4) = 10(7 - 5.4). Each seller's output is 1/10 of this quantity.

(e) [15 marks] Compute the consumer surplus and producer surplus under the cartel. Consumer surplus is now the area between the demand curve and the cartel price line, up to the quantity demanded at the cartel price. Producer surplus is the area between the cartel price line and the supply curve, up to the quantity supplied at the cartel price.

(f) [5 marks] Explain why the sellers prefer operating under a cartel to competing with each other without legal restrictions. (Limited to 50 words.) Sellers prefer operating under a cartel because it allows them to collectively act as a monopoly, setting a higher price and earning more profit than they would under perfect competition.

(g) [5 marks] Explain why the cartel is detrimental to the entire society. (Limited to 100 words.) A cartel is detrimental to society because it results in a higher price and lower quantity than under perfect competition. This leads to a loss of consumer surplus, which is not fully offset by the increase in producer surplus. The result is a deadweight loss, representing a reduction in total social welfare.