Carmen is a writer who enjoys writing with both pencils and pens. Her utility function for pencils and pens is given by U = 4X + 2Y, where X is the number of pencils she buys and Y is the number of pens. Carmen currently has 2 pencils and 4 pens.

a. Calculate Carmen’s current utility.

b. What is the marginal utility of an additional pencil, MU_X? An additional pen, MU_Y?

c. Find two other bundles of pencils and pens that would give Carmen the same level of satisfaction she currently has, and connect the dots to create an indifference curve. Does the indifference curve have a special shape? Why might it have this shape?

d. The marginal rate of substitution (MRS) is measured as the slope of an indifference curve. Calculate the MRS at Carmen’s current consumption level. Does it equal the ratio of marginal utilities, MU_X/MU_Y?