Question

1. Suppose a consumer's preference over consumption (C) and leisure (1) can be described by a utility function: U (1,c) = Inl+c. Her budget constraint can be written as: c=E+w(L-1). All notations have the same interpretation as in my lecture notes, Section 13E.1. a. (3 points) Solve her demand for leisure. b. (2 points) How does her labor supply decision depend on the wage rate w?

Answer 1

a. The consumer's problem is:

max Inl+ st. C + WIE + WL

At equilibrium, marginal rate of substitution is equal to the price ratio:

MRS ==W - W1 = 1

Substituting this into the consumer's budget equation:

1+0=E+WI+C=E+wi - 1,1 =

b. The consumer's labor supply is given by:
$\small l=\frac{1}{w}$
Differentiating with respect to w:

Therefore, if the wage rate goes up by one unit, the consumer's labor supply falls by the above amount.

dl 1 dw we