3. Consider the individual's utility function: U = U(C, L) = L Ch (a) Compute the Marshallian labour supply. (b) Briefly discuss the main properties of this function.

When deriving labour supply, we assumed that the substitution effect dominated the income effect. What impact would there be on labour supply if this was not the case? Briefly investigate how such a change could theoretically affect the imposition of a minimum wage. (Your answer is likely to benefit if it is supported by a diagram.)

1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings. Assume that the price of x equals 1. a) Specify the utility maximization problem, write down the Lagrange function, and solve for the first order conditions. b) Solve for the MRS condition between consumption and hours of work. c) Assume that 8=2 if the person has a child living at home, and 8=1 otherwise. Explain (and either show mathematically or graphically) how this will affect the optimal number of hours of work of the person.

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