7. Arnold Schwarzenegger and Fernand Leger have been stranded on a desert island. The only foods available to them are oranges and blackberries. Schwarzenegger is endowed with 2 oranges and 5 blackberries, while Leger is endowed with 10 oranges and 1 blackberry. Both Schwarzenegger and Leger have Cobb-Douglas preferences with a = B = 1. Let pl and p2 be the prices of oranges and blackberries, respectively. Let xC1 and xC2 be Schwarzenegger's demand for oranges and blackberries, respectively, and xF1 and xF2 be Leger's demand for oranges and blackberries, respectively. (a) What are Schwarzenegger's and Leger's demand functions for oranges and blackberries? Your answer should be in terms of prices pl and p2. (b) Find the competitive equilibrium. (c) Is the allocation Pareto efficient? Explain. (d) What is the marginal rate of substitution between oranges and blackberries? (e) Suppose that before the trade, Leger discovers 6 new oranges on the other side of the island. How many oranges would he have to give to Schwarzenegger so that they would both have the same utility in equilibrium? 7. Arnold Schwarzenegger and Fernand Leger have been stranded on a desert island. The only foods available to them are oranges and blackberries. Schwarzenegger is endowed with 2 oranges and 5 blackberries, while Leger is endowed with 10 oranges and 1 blackberry. Both Schwarzenegger and Leger have Cobb-Douglas preferences with a = B = 1. Let pl and p2 be the prices of oranges and blackberries, respectively. Let xC1 and xC2 be Schwarzenegger's demand for oranges and blackberries, respectively, and xF1 and xF2 be Leger's demand for oranges and blackberries, respectively. (a) What are Schwarzenegger's and Leger's demand functions for oranges and blackberries? Your answer should be in terms of prices pl and p2. (b) Find the competitive equilibrium. (c) Is the allocation Pareto efficient? Explain. (d) What is the marginal rate of substitution between oranges and blackberries? (e) Suppose that before the trade, Leger discovers 6 new oranges on the other side of the island. How many oranges would he have to give to Schwarzenegger so that they would both have the same utility in equilibrium