Hi! could you help me with this? K, the variable are different from the ones on your site.. thank you

1. Vanna Boogie likes to have large parties. She also has a strong preference for having exactly as many men as women at her parties. In fact, Vanna's preferences among parties can be represented by the utility function U(x; y) = min{3x - y; 3y- x} where x is the number of women and y is the number of men at the party. On the graph below, let us try to draw the indifference curve along which Vanna's utility is 15.

(a) Use pen to draw the locus of points at which x = y. What point on this gives Vanna a utility of 15? Use broken line to draw the line along which 3y - x = 15. When min{3x - y; 3y- x} = 3y - x, there are (more men than women, more women than men)? Draw a bold solid line over the part of the broken line for which U(x; y) = min{3x-y; 3y -x} = 3y-x. This shows all the combinations that Vanna thinks are just as good as (15; 15) but where there are (more men than women, more women than men)? Now draw a broken line along which 3x - y = 15. Draw a bold solid line over the part of this new broken line for which min{3x-y; 3y-x} = 3x-y. Use pen to shade in the area on the graph that represents all combinations that Vanna likes at least as well as (15; 15).

(b) Suppose that there are 9 men and 10 women at Vanna's party. Would Vanna think it was a better party or a worse party if 5 more men came to her party?

(c) If Vanna has 16 women at her party and more men than women, and if she thinks the party is exactly as good as having 10 men and 10 women, how many men does she have at the party? If Vanna has 16 women at her party and more women than men, and if she thinks the party is exactly as good as having 10 men and 10 women, how many men does she have at her party?

(d) Vanna's indifference curves are shaped like what letter of the alphabet?

2. Nancy Lerner is trying to decide how to allocate her time in studying for her economics 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 2,400 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 if she doesn't study at all, she will get a score of zero on it. For every 20 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. For every 40 minutes she spends studying for the second examination, she will increase her score by one point.

(a) On a graph draw a "budget line" showing the various combinations of scores on the two exams that she can achieve with a total of 2,400 minutes of studying. On the same graph, draw two or three "indifference curves" for Nancy. On your graph, draw a straight line that goes through the kinks in Nancy's indifference curves. Label the point where this line hits Nancy's budget with the letter A. Draw Nancy's indifference curve through this point.

(b) function for Nancy's indifference curves (her utility function).

(c) equation for Nancy's budget line.

(d) Given Nancy's budget line and her utility function, what is her best choice under these conditions?

3. Mary's utility function is U(b; c) = b + 100c - c², where b is the number of silver bells in her garden and c is the number of cockle shells. She has 500 square feet in her garden to allocate between silver bells and cockle shells. Silver bells each take up 1 square foot and cockle shells each take up 4 square feet. She gets both kinds of seeds for free.

(a) To maximize her utility, given the size of her garden, how many silver bells and cockle shells should Mary plant respectively?

(b) If she suddenly acquires an extra 100 square feet for her garden, how much should she increase her planting of silver bells?How much should she increase her planting of cockle shells?

(c) If Mary had only 144 square feet in her garden, how many cockle shells would she grow?

(d) If Mary grows both silver bells and cockle shells, then we know that the number of square feet in her garden must be greater than.

4. Neville's passion is fine wine. When the prices of all other goods are fixed at current levels, Neville's demand function for highquality claret is q = 0.02m - 2p, where m is his income, p is the price of claret (in British pounds), and q is the number of bottles of claret that he demands. Neville's income is 10,000 pounds, and the price of a bottle of suitable claret is 40 pounds.

(a) How many bottles of claret will Neville buy?

(b) If the price of claret rose to 50 pounds, how much income would Neville have to have in order to be exactly able to afford the amount of claret and the amount of other goods that he bought before the price change? At this income, and a price of 50 pounds, how many bottles would Neville buy?

(c) At his original income of 10,000 and a price of 50, how much claret would Neville demand?

(d) When the price of claret rose from 40 to 50, the number of bottles that Neville demanded decreased by. The substitution effect (increased, reduced)his demand bybottles and the income effect (increased, reduced)his demand by.