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Over the last several years, a number of municipalities in California have adopted restrictions on the bags that grocers are allowed to give to customers.

Over the last several years, a number of municipalities in California have adopted restrictions on the bags that grocers are allowed to give to customers. The nature of the restrictions varies by municipality, but generally, a customer must either provide his or her own bags, or the store is required to charge some minimum price for bags.
-A recent paper finds that one of the consequences of these policies is an increase of roughly one minute in the time required for “checkout” of each customer.
-Suppose that consumers value both consumption of groceries (c), leisure (L), and other goods (z) according to an ordinal utility function U(c, L , z) = α log c + β   log L + γ log z.
-All consumers have 24 hours in a day, which they can devote to leisure, to work, or to shopping.
-For each hour a consumer works he or she earns a wage w. For each bag of groceries purchased the consumer must spend 10 minutes in the absence of bag restrictions, and pay a price p per bag. Take “other goods” z to be num ́eraire (i.e., the price of z is one). Suppose that in addition to labor earnings the consumer also has non-labor income x.
–             ****If unable to answer all, please can you help in answering a.) ? ****
-a)  Formulate the problem facing the consumer; in particular, how are constraints on time and money related?
-b)  Derive an expression for the marginal rate of substitution between groceries and leisure.
-c)  Calculate Marshallian demand functions for groceries, leisure, and other goods. How do these depend on bag restrictions?
-d)  Suppose that consumers are all identical, but that rich consumers have twice as much non-labor income as poor consumers. Do the bag restrictions a↵ect rich and poor differently? (Explain precisely, using the Marshallian demand functions you’ve derived).   Due Tues Sept 27 1pm PST

 
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