Y7

1. Matthew has applied for an educational grant to study economics abroad. He has won the grant, and now every month he has $400 of spare cash to spend on goods and services of his own choice (we assume that the indispensable costs of tuition, rent, utilities etc. are already covered by the grant). Every month, Matthew's studies leave him 100 hours of spare time, which he can use for either leisure or giving private economics lessons to other students for an hourly wage of $w. Let "c" denote Matthew's monthly spending on goods and services of his own choice (in dollars), and let "(" denote the duration of his monthly leisure time (in hours). Suppose Matthew's preferences are standard, and both "c" and "/" are normal goods for him. A) Write down Matthew's budget line equation. Using a properly labeled graph with "/" on the horizontal axis and "c" on the vertical, illustrate Matthew's budget set. Indicate Matthew's optimal consumption bundle on your graph, assuming that he allocates 60 hours of his spare time to giving private lessons. B) Suppose Matthew's utility function is U(c, /) = 200 / +c. (i) Find the value of Matthew's reservation wage (i.e., the minimal hourly wage we that he would accept for giving private economics lessons). (il) Write down Matthew's utility maximization problem. Derive and illustrate Matthew's labor supply curve (you can rely on the fact that his preferences are standard)