For both of the following utility functions, draw the indifference curves for the indicated utility levels, including at least three consumption bundles on each. Be precise. (And don’t expect the indifference curves to necessarily look like those in class.)

a. i) u(x,y) = xy ( MUx=y, MUy=x ) for 16 utils and 25 utils ii) u(x,y) = 6x+2y ( MUx=6, MUy=2 ) for 30 utils and 60 utils

b. Suppose the person in part a(i) is currently consuming 100 units of x and 50 units of y. Using this person’s utility function, determine how much additional utility she would get if she were to increase her consumption of x by 1 unit? How does this relate to the formulas given in parentheses in part a(i)?

c. Derive the formula for the marginal rate of substitution for each of the people in part a.

d. For each utility function, what is the slope of the indifference curve at the bundle (2,4) and at (4,1)?

For both of the following utility functions, draw the indifference curves for the indicated utility levels, including at least three consumption bundles on each. Be precise. (And don’t expect the indifference curves to necessarily look like those in class.)

a. i) u(x,y) = xy ( MUx=y, MUy=x ) for 16 utils and 25 utils ii) u(x,y) = 6x+2y ( MUx=6, MUy=2 ) for 30 utils and 60 utils

b. Suppose the person in part a(i) is currently consuming 100 units of x and 50 units of y. Using this person’s utility function, determine how much additional utility she would get if she were to increase her consumption of x by 1 unit? How does this relate to the formulas given in parentheses in part a(i)?

c. Derive the formula for the marginal rate of substitution for each of the people in part a.

d. For each utility function, what is the slope of the indifference curve at the bundle (2,4) and at (4,1)?