Lady Wellesleigh makes silk purses out of sows’ ears. She is the only person in the world who knows how to do so. It takes one sow’s ear and 1 hour of her labor to make a silk purse. She can buy as many sows’ ears as she likes for $1 each. Lady Wellesleigh has no other source of income than her labor. Her utility function is a Cobb-Douglas function U(c, r) = c1/3r2/3, where c is the amount of money per day that she has to spend on consumption goods and r is the amount of leisure that she has. Lady Wellesleigh has 24 hours a day that she can devote either to leisure or to working.
(a) Lady Wellesleigh can either make silk purses or she can earn $5 an hour as a seamstress in a sweatshop. If she worked in the sweat shop, how many hours would she work? _____.
(b) If she could earn a wage of $w an hour as a seamstress, how much would she work? ______.
(c) If the price of silk purses is $p, how much money will Lady Wellesleigh earn per purse after she pays for the sows’ ears that she uses? _____.
(d) If she can earn $5 an hour as a seamstress, what is the lowest price at which she will make any silk purses? _____.
(e) What is the supply function for silk purses?