Consider two consumers (1; 2), each with income M to allocate between two goods. Good 1 provides 1 unit of consumption to its purchaser and units of consumption to the other consumer. Each consumer i, i = 1; 2, has the utility function is consumption of good 1 and is consumption of good 2. a. Provide an interpretation of α. b. Suppose that good 2 is a private good. Find the Nash equilibrium levels of consumption when both goods have a price of 1. c. By maximizing the sum of utilities, show that the equilibrium is Pareto-ancient if α = 0 but incident for all other values of α. d. Now suppose that good 2 also provides 1 unit of consumption to its purchaser and a, 0 ≤ α ≤ 1, units of consumption to the other consumer. For the same preferences, find the Nash equilibrium and show that it is ancient for all values of α. e. Explain the conclusion in part d.
Consider two consumers (1; 2), each with income M to allocate between two goods. Good 1 provides 1 unit of consumption to its purchaser and 
units of consumption to the other consumer. Each consumer i, i = 1; 2, has the utility function 
is consumption of good 1 and 
is consumption of good 2.
a. Provide an interpretation of α.
b. Suppose that good 2 is a private good. Find the Nash equilibrium levels of consumption when both goods have a price of 1.
c. By maximizing the sum of utilities, show that the equilibrium is Pareto-ancient if α = 0 but incident for all other values of α.
d. Now suppose that good 2 also provides 1 unit of consumption to its purchaser and a, 0 ≤ α ≤ 1, units of consumption to the other consumer. For the same preferences, find the Nash equilibrium and show that it is ancient for all values of α.
e. Explain the conclusion in part d.
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