Can I get more explanation on how to graph a typical indifference curve for the following utility?

1. Determine weather each of the following statement is "true" or "false" .

(a) Indifference curves may sometimes intersect.

(b) If bundles of goods A and B lie on the same indifference curve, one can assume the individual enjoys bundle A and B equally.

(c) If bundles of goods A and B lie on the same indifference curve, one can assume the individual bundle A contains the same goods as bundle B. (d) U(x,y)= 4x + 2y For this utility function, the MRS is always 2.

(e) U(x,y)= min (x, 2y) For this utility function, the MRS is always 2.

2. Sarah consumes apples and oranges (these are the only fruits she eats). She has decided that her monthly budget for fruit will be $50. Suppose that one apple costs $0.25, while one orange costs $0.50. Let x denote the quantity of apples and y denote the quantity of oranges that Sarah purchases.

(a) What is the expression for Sarah's budget constraint?

(b) Draw a graph of Sarah's budget line.

(c) Show graphically how Sarah's budget line changes if the price of apples increases to $0.50.

(d) Show graphically how Sarah's budget line changes if the price of oranges decreases to $0.25.

(e) Suppose Sarah decides to cut her monthly budget for fruit in half. Coincidentally, the next time she goes to the grocery store, she learns that oranges and apples are on sale for half price, will remain so for the next month, i.e., the price of apples falls from $0.25 per apple to $0.125 per apple and the price of oranges falls from $0.50 per orange to $0.25 per orange.What happens to the graph of Sarah's budget line?

3. Graph a typical indifference curve for the following utility functions (set utility to something like 1,10 or any other numbers so you can graph it), and determine whether they have diminishing MRS. (i.e., whether the MRS declines as x increases).

(a) U(x, y) = 3x + y.

(b) U(x, y) = x y.

(c) U(x, y) = x + y.

(d) U(x, y) = p x 2 y 2.

(e) U(x, y) = xy x+y