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A representative consumer living in a Country A values consuming goods (C) and enjoys leisure (l)....

A representative consumer living in a Country A values consuming goods (C) and enjoys leisure (l). The consumer has h = 1 units of time to divide between working and enjoying leisure. For each hour worked, he receives w = 1.5 units of the consumption good. The consumer also owns shares in a factory which gives him an additional π = 0.55 units of income. The government in this economy taxes the consumer and uses the proceeds to buy consumption goods that are given to the army. The consumer pays a lump sump tax T equal to 0.35. Suppose that the consumer’s preferences are described by the the utility function.

U(C, l) = C ^1/3 + L ^1/3

1. Write down and graph the consumer’s budget constraint.

2. Define and compute the MRS as a function of C and l.

3. Is it optimal for the consumer to supply Ns = 0.8 units of labour?

4. Find the consumer’s optimal choice of consumption and leisure. Illustrate with a graph.

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