Jack and Jill, who usually pump water from their wells to sell at the market, have...

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Jack and Jill, who usually pump water from their wells to sell at the market, have also noticed that the wells are located in the middle of groves of apple trees. Never ones to turn down an opportunity to make some money, they realize they can pick apples while they wait for the water to pump and sell those at the market as well. For simplicity, assume that the cost of bringing apples to the market is zero and that the demand for apples is given below. Quantity Price: Total Revenue (and total profit) 0 $24 50 1 22 22 2 20 40 3 18 54 4 16 64 S 14 b 12 7 To 70 72 70 8 8 64 9 6 54 10 4 40 2 22 0 0 11 12 To see how the welfare outcome of this duopoly stacks up (and to review concepts from earlier units from class), let's first consider the two extreme benchmarks that we've examined: perfect competition and monopoly. (Hint: feel free to draw graphs for parts (a-d) and assume demand is linear.) (a) (2 points) Suppose that, instead of Jack and Jill controlling the apple groves, the apple market is perfectly competitive. If the cost of supplying apples stayed at zero, what would the price and quantity sold be? (b) (4 points) What would total surplus be under perfect competition? (c) (2 points) Now, suppose instead that a monopolist controls apple production in the village. Again, assume that costs remain unchanged. What would the monopolist's price and level of output be? (d) (4 points) What would total surplus be under a monopolist? Now, let's consider the situation at hand. Suppose that Jack and Jill must each decide in the morning how many apples to take to market, and the apples will be sold at the market-clearing price. (e) (4 points) If they attempt to collude, what is the most they could possibly earn in total? To achieve this, how many apples should they bring to the market in total? (f) (6 points) Suppose that Jack and Jill have agreed to collude by each supplying half of the monopoly quantity from part (c). If Jack were to stick to the deal, what happens to Jill's profit if she instead supplies an extra apple in addition to her agreed-upon quantity? Should we expect Jack and Jill to stick to their agreement? (Hint: Recall that the total quantity determines the price, and each person's profit is then determined by the quantity they individually supply.) (g) (4 points) On the other hand, show that if Jack and Jill are each planning to bring 4 apples with them to market, then neither of them wants to bring one less apple or one more apple. In other words, show that this is the Nash equilibrium of this Cournot oligopoly. (h) (4 points) How does total welfare under this oligopoly equilibrium compare to the outcomes under monopoly and under perfect competition? (Hint: It may be helpful to draw simple graphs of the three outcomes.) Jack and Jill, who usually pump water from their wells to sell at the market, have also noticed that the wells are located in the middle of groves of apple trees. Never ones to turn down an opportunity to make some money, they realize they can pick apples while they wait for the water to pump and sell those at the market as well. For simplicity, assume that the cost of bringing apples to the market is zero and that the demand for apples is given below. Quantity Price: Total Revenue (and total profit) 0 $24 50 1 22 22 2 20 40 3 18 54 4 16 64 S 14 b 12 7 To 70 72 70 8 8 64 9 6 54 10 4 40 2 22 0 0 11 12 To see how the welfare outcome of this duopoly stacks up (and to review concepts from earlier units from class), let's first consider the two extreme benchmarks that we've examined: perfect competition and monopoly. (Hint: feel free to draw graphs for parts (a-d) and assume demand is linear.) (a) (2 points) Suppose that, instead of Jack and Jill controlling the apple groves, the apple market is perfectly competitive. If the cost of supplying apples stayed at zero, what would the price and quantity sold be? (b) (4 points) What would total surplus be under perfect competition? (c) (2 points) Now, suppose instead that a monopolist controls apple production in the village. Again, assume that costs remain unchanged. What would the monopolist's price and level of output be? (d) (4 points) What would total surplus be under a monopolist? Now, let's consider the situation at hand. Suppose that Jack and Jill must each decide in the morning how many apples to take to market, and the apples will be sold at the market-clearing price. (e) (4 points) If they attempt to collude, what is the most they could possibly earn in total? To achieve this, how many apples should they bring to the market in total? (f) (6 points) Suppose that Jack and Jill have agreed to collude by each supplying half of the monopoly quantity from part (c). If Jack were to stick to the deal, what happens to Jill's profit if she instead supplies an extra apple in addition to her agreed-upon quantity? Should we expect Jack and Jill to stick to their agreement? (Hint: Recall that the total quantity determines the price, and each person's profit is then determined by the quantity they individually supply.) (g) (4 points) On the other hand, show that if Jack and Jill are each planning to bring 4 apples with them to market, then neither of them wants to bring one less apple or one more apple. In other words, show that this is the Nash equilibrium of this Cournot oligopoly. (h) (4 points) How does total welfare under this oligopoly equilibrium compare to the outcomes under monopoly and under perfect competition? (Hint: It may be helpful to draw simple graphs of the three outcomes.)