Suppose social well-being is determined by the function u(x1, x2, ..., XN) where x; is the...

  

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Suppose social well-being is determined by the function u(x1, x2, ..., XN) where x; is the quantity of public service i provided by the government. a) (3 points) How many first order partial derivatives does u have? Pick one of these and explain in words what it represents, in the context of social well-being and public service provision. For the rest of the problem, consider the simplified version with two ser- vices, V = u(x, y). Let x be urban green spaces and y national parks. b) (2 points) With the current level of urban green spaces and national parks provided, social well-being is W. Describe in words what the level curve u(x, y) = W represents, in the context of urban green spaces and national parks. %3D c) (4 points) Let y f(x) be this level curve. Using implicit differenti- ation, find f'(x). What is its sign? Explain with economic intuition. d) (1 point) Suppose each urban green space costs p to maintain and each national park q. Write the cost function c(x,y) of maintaining x urban green spaces and y national parks. Suppose social well-being is determined by the function u(x1, x2, ..., XN) where x; is the quantity of public service i provided by the government. a) (3 points) How many first order partial derivatives does u have? Pick one of these and explain in words what it represents, in the context of social well-being and public service provision. For the rest of the problem, consider the simplified version with two ser- vices, V = u(x, y). Let x be urban green spaces and y national parks. b) (2 points) With the current level of urban green spaces and national parks provided, social well-being is W. Describe in words what the level curve u(x, y) = W represents, in the context of urban green spaces and national parks. %3D c) (4 points) Let y f(x) be this level curve. Using implicit differenti- ation, find f'(x). What is its sign? Explain with economic intuition. d) (1 point) Suppose each urban green space costs p to maintain and each national park q. Write the cost function c(x,y) of maintaining x urban green spaces and y national parks.