microeconomics utility consumers optimal choice

Here is a preview of the tasks, all the information and graphs are in the document attached.

1. A consumer’s utility function is given by U = XY . a. What is the utility derived from 1 unit of X and 2 units of Y ? What is the utility derived from 2 units of X and 1 units of Y ? What is the utility derived from 5 units of X and 2 units of Y ? b. How does the consumer rank the following bundles?

4. Remember Anny Knowsmuch? Now she is trying to decide how to allocate her time in studying for her technology course. There are two examinations in this course. Her overall score for the course will be the minimum of her scores on the two examinations. She has decided to devote a total of 1,200 minutes to studying for these two exams, and she wants to get as high an overall score as possible. She knows that on the first examination id she doesn’t study at all, she will get a score of zero on it. For every 10 minutes that she spends studying for the first examination, she will increase her score by one point. If she doesn’t study at all for the second examination she will get a zero on it. Foe every 20 minutes she spends studying for the second examination, she will increase her score by one point. a. On the graph below, draw a “budget line” showing the various combinations of scores on the two examns that she can achieve with a total of 1,200 minutes of studying. On the same graph, draw two or three “indifference curves” for Anny. On your graph, draw a straight line that goes through the kinks in 2 Anny’s indifference curves. Label the point where this line hits Anny’s budget with the letter A. Draw Anny’s indifference curve through this point

6. Andrea spends his income on tennis balls (B) and guitar picks (P). Tennis balls are priced at $10, while a package of guitar picks costs $3. Assume that Andrea has $50 to spend and his utility function can be represented as U(B, P) = B0.5P 0.5 . a. What is the optimal number of tennis balls and guitar picks for Andrea to purchase? How much utility does this combination bring him? b. If the price of guitar picks doubles to $6, how much income must Andrea have to maintain the same level of utility? c. In a graph draw what happens to the optimal choice if the price of tennis balls increases to $13. Find the new optimal choice (mathematically)

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