Homework $3$ Consumer Behavior

Mylie's total utility from singing the same song over and over is $50$ utils after one repetition, $90$ utils after two repetitions, $70$ utils after three repetitions, $20$ utils after four repetitions, $-50$ utils after five repetitions, and $-200$ utils after six repetitions. Write down her marginal utility for each repetition. Once Mylie's total utility begins to decrease, does each additional singing of the song hurt more than the previous one or less than the previous one?

John likes Coca$-$Cola. After consuming one Coke, John has a total utility of $10$ utils. After two Cokes, he has a total utility of $25$ utils. After three Cokes, he has a total utility of $50$ utils. Does John show diminishing marginal utility for Coke or does he show increasing marginal utility for Coke? Suppose that John has $$3$ in his pocket. If Cokes cost $$1$ each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John's marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?

$3-0]$i$-$J$0.$ You are choosing between two goods, X and Y $,$ and your marginal utility from each is as shown in the table below. If your income is $$9$ and the prices of X and Y are $$2$ and $$1,$ respectively, what quantities of each will you purchase to maximize utility? What total utility will you realize? Assume that, other things remaining unchanged, the price of $x$ falls to $$1.$ What quantities of $x$ and $Y$ will you now purchase? Using the two prices and quantities for X $,$ derive a demand schedule $($prices and quantities demanded table$)$ for $x.$

$\backslash$table$[[$Units of X$,()z,$Units of Y$,()y$