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 = 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. [03 points]

2. Define and compute the MRS as a function of C and l. [03 points]

3. Is it optimal for the consumer to supply Ns = 0.8 units of labour? [03 points]

4. Find the consumer's optimal choice of consumption and leisure. Illustrate with a graph. [06 points]