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3. social planners problem two constraints 1 five units of good...

Question: social planners problem two constraints 1 five units of good...

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Social planner’s problem, two constraints 1

Five units of good 1 and five units of good 2 are available. Consumption of good 1 is denoted x_1 and consumption of good 2 by x_2. There are two agents: A and B. Their utility functions are u_A(x_1, x_2) = ln(x_1) +a*ln(x_2) and u_B(x_1, x_2) = x_1 +b*x_2, where a=0.54 and b=1.52. Here, ln denotes the natural logarithm, * multiplication, + addition.

Maximize u_A subject to the constraints u_B=1 and that each agent’s consumption of each good is nonnegative. Write the quantity x_1 of good 1 that agent A consumes in the solution to the maximisation problem. Write it as a number in decimal notation with at least two digits after the decimal point. No fractions, spaces or other symbols.

Two constraints bind because of the a, b chosen.