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 minuts in the absence of bag restrictions, and pay a price p per bag. Take "other goods" z to be numeraire"(i.e., the price of z is one). Duppose that in addition to labor earnings the consumer also has non-labor income x.
a) Firmulate 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 ans leisure.
c) Calculate Marshallian for the margianl rate of substitution between groceries and leisure, and other goods. How do these depend on bag restrictions?
d) Suppose that consumers are all idential, but that rich consumers have twice as much non-labor income as poor consumers. Do the bag restrictions affect rich and poor differently?(Explain precisely, using the Marchallian demand functions you've derived)