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) =[ + ()]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.