# Question: In this chapter we showed an example in which the

In this chapter, we showed an example in which the consumer has preferences for consumption with the perfect complements property. Suppose, alternatively, that leisure and consumption goods are perfect substitutes. In this case, an indifference curve is described by the equation

i = al + bC,

where a and b are positive constants, and u is the level of utility. That is, a given indifference curve has a particular value for u, with higher indifference curves having higher values for u.

(a) Show what the consumerâ€™s indifference curves look like when consumption and leisure are perfect substitutes, and determine graphically and algebraically what consumption bundle the consumer chooses. Show that the consumption bundle the consumer chooses depends on the relationship between a/b and w, and explain why.

(b) Do you think it likely that any consumer would treat consumption goods and leisure as perfect substitutes?

(c) Given perfect substitutes, is more preferred to less? Do preferences satisfy the diminishing marginal rate of substitution property?

i = al + bC,

where a and b are positive constants, and u is the level of utility. That is, a given indifference curve has a particular value for u, with higher indifference curves having higher values for u.

(a) Show what the consumerâ€™s indifference curves look like when consumption and leisure are perfect substitutes, and determine graphically and algebraically what consumption bundle the consumer chooses. Show that the consumption bundle the consumer chooses depends on the relationship between a/b and w, and explain why.

(b) Do you think it likely that any consumer would treat consumption goods and leisure as perfect substitutes?

(c) Given perfect substitutes, is more preferred to less? Do preferences satisfy the diminishing marginal rate of substitution property?

## Answer to relevant Questions

Consider the consumer choice example in this chapter, where consumption and leisure are perfect complements. Assume that the consumer always desires a consumption bundle where the quantities of consumption and leisure are ...Show that the consumer is better off with a lump-sum tax rather than a proportional tax on wage income (as in question) given that either tax yields the same revenue for the government. You must use a diagram to show this.Suppose a firm has a production function given by Y = zK0.3 N0.7.(a) If z = 1 and K = 1, graph the production function. Is the marginal product of labor positive and diminishing?(b) Now, graph the production function when z ...Suppose that government spending makes private firms more productive; for example, government spending on roads and bridges lowers the cost of transportation. This means that there are now two effects of government spending, ...Adapt the DMP model to include government activity as follows. Suppose that the government can operate firms, subject to the same constraints as private firms. In particular, the government must incur a cost k to post a ...Post your question