PAST TEST:

Consider a utility maximization problem of the representative consumer who makes a choice between consumption C and leisure l. Assume that the consumer's preferences are defined by the following utility function

U(C,l) =[C+a ln(l)]^0.5, where a >0 [utility]

The consumer is endowed with h units of time. The consumer lives one period. The consumer spends the time either working on the market or by taking leisure. The consumer receives the real wage w for each unit of labour supplied. Denote the labour supply by N. The consumer pays the lump sum tax T and receives the real dividends payments . Assume that - T>0.

Answer all parts of this question using the utility function provided in the description above.

a) Compute the marginal utility of consumption UC(C,l) and the marginal utility of leisure Ul(C,l). Do the consumer's preferences satisfy the assumption that more is always preferred to less? Explain your response.

b) Compute the marginal rate of substitution of leisure for consumption, MRSl,C. Is the marginal rate of substitution diminishing? What does your answer imply about the shape of the indifference curves? Illustrate the indifference curves in the space with leisure on the horizontal axis and consumption of the vertical axis.

c) Give a mathematical formulation of the consumer's optimization problem. That is, state explicitly the consumer's goal, constraint(s) and indicate the consumer's choice variables.

d) Which two mathematical conditions define the consumer's optimal choice of consumption and leisure? Explain the economic meaning of these conditions.

e) Find the optimal values of C* and l* as functions of the exogenous variables and model parameters (i.e. solve the consumer's optimization problem).

f) Consider a stock market bust that decreases the value of dividends. Analyze the impact of this stock market bust on the optimal consumption C*, leisure l* and labour supply N*. Illustrate your response graphically. Are your predictions consistent with the assumption that consumption and leisure normal goods? Explain your response.