2.1 Suppose U(x, y) 4x2 3y 2 . a. Calculate @U/@x, @U/@y. b. Evaluate these partial derivatives at x 1, y

2.1 Suppose U(x, y) ¼ 4x2 þ 3y 2

.

a. Calculate @U/@x, @U/@y.

b. Evaluate these partial derivatives at x ¼ 1, y ¼ 2.

c. Write the total differential for U.

d. Calculate dy/dx for dU ¼ 0—that is, what is the implied trade-off between x and y holding U constant?

e. Show U ¼ 16 when x ¼ 1, y ¼ 2.

f. In what ratio must x and y change to hold U constant at 16 for movements away from x ¼ 1, y ¼ 2?

g. More generally, what is the shape of the U ¼ 16 contour line for this function? What is the slope of that line?