Problem 6.1

Please answer this question with calculations.

Agent X can allocate leisure (h) and consumption (c) over a 24h period. Agent X receives a $60 payment every day from a life-long prize he won times ago. The price of consumption is $1. Agent X utility function is given by the function: U(c, h) = c^1/2 h^1/4. [1] If the market wage for Agent X is $10, based on the information provided, how many hours he will works? [2] What is Agent X general demand for leisure? Find it as a function of w (market wage). [3] Find a function (using the leisure demand function in part [2]) for Agent X individual labor supply. [4] Lastly, using the derivative of Agent X individual labor supply, find the size of the income and substitution effect of Agent X demand for leisure.