Suppose Ana consumes consumes only baguettes, vegetables and chocolates.

Suppose Ana consumes consumes only baguettes, vegetables and chocolates. Let x denote her baguette consumption per month in kg, y denote her vegetable consumption per month in kg, and z denotes her chocolate consumption in kg. Anas preference can be represented by U (x;y;z) = logx + logy + log(1 + z). Suppose also that the prices for these goods are given by px = 1, py = 3 and pz = 12 and that Ana has a monthly income of I = 12. Suppose chocolates are not available in the summer due to the heat. So all summer, z is forced to be 0. 

 Suppose this summer, price of vegetables have risen to $4/kg in the city of Pugwash where Ana lives. This creates widespread dissatisfaction. Suppose the city government of Pugwash decides to give a $1=kg subsidy to vegetables. With this subsidy, residents of Pugwash pay only $3=kg for their vegetables, while the government pay so $1=kg for its residents vegetable consumption. What is the total amount of subsidy that Ana receives per month from the government? On a graph with x on the horizontal axis and y on the vertical axis, mark Anas budget line, optimal consumption bundle, and the indifference that passes through it.