4. (Optional: the following exercise relates to a paper that may be relevant later on in the course. If you are not interested in the topic, feel free to skip the exercise). Dubois et al. (2014) develop a demand system to study the drivers of the differences $101 Public Economics 1 in food purchases across countries. The underlying utility in their demand system is given by J K₂ (2, 2012) (4) (4) (100) Pij where J denotes the number of food categories being studied and K; the different brands/barcodes there are within each food category j € {1,...,J}. z; is the nu- meraire good, z; is a C x 1 vector of characteristics of food and 9 is a vector of quantities purchased of all food products by household i. Define the N x C matrix A = {n} The household maximizes its utility by choosing the quantity of the numeraire ; and of food items q; subject to a budget constraint N poti + Puginti, n=1 % and a "resource" constraint stating that the household gets the nutrients specified by the quantities it consumes of each good, namely, Noriko Amano-Patiño z = A'gi- Try to follow their model and derive the expression in equation (2) (stated below) from the solution to the optimization problem of the household. ΣPejqikj=po² + IMG Po IMA akjclikj.

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4. (Optional: the following exercise relates to a paper that may be relevant later on in the course. If you are not interested in the topic, feel free to skip the exercise). Dubois et al. (2014) develop a demand system to study the drivers of the differences $101 Public Economics 1 in food purchases across countries. T