# Question: Extend the model of public goods in the last section

Extend the model of public goods, in the last section of this chapter, as follows. Suppose that output is produced, as in the simplified model with proportional taxation, only with labor, and that z = 1. Here, however, there is lump-sum taxation, and the PPF is given by Y = h – l – G. Now the consumer has preferences over three goods: private goods C, public goods G, and leisure l. Assume that C and l are perfect complements for the consumer, that is, the consumer always wants to consume C and l in fixed proportions, with C = dl, and d > 0.

(a) Suppose, just as in part (a) of problem 11, that public goods and private goods are perfect substitutes. Determine the effects of an increase in G on consumption and labor supply, and explain your results.

(b) Alternatively, assume, just as in part (b) of problem 11, that public goods and private goods are perfect complements. Again, determine the effects of an increase in G on consumption and labor supply, and explain your results.

(a) Suppose, just as in part (a) of problem 11, that public goods and private goods are perfect substitutes. Determine the effects of an increase in G on consumption and labor supply, and explain your results.

(b) Alternatively, assume, just as in part (b) of problem 11, that public goods and private goods are perfect complements. Again, determine the effects of an increase in G on consumption and labor supply, and explain your results.

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