The utility that Ann receives by consuming food F and clothing C is given by U(F, C) = FC + F. The marginal utilities of food and clothing are MUF = C + 1 and MUC = F. Food costs $1 a unit, and clothing costs $2 a unit. Ann's income is $22.
a) Ann is currently spending all of her income. She is buying 8 units of food. How many units of clothing is she consuming?
b) Graph her budget line. Place the number of units of clothing on the vertical axis and the number of units of food on the horizontal axis. Plot her current consumption basket.
c) Draw the indifference curve associated with a utility level of 36 and the indifference curve associated with a utility level of 72. Are the indifference curves bowed in toward the origin?
d) Using a graph (and no algebra), find the utility maximizing choice of food and clothing.
e) Using algebra, find the utility-maximizing choice of food and clothing.
f) What is the marginal rate of substitution of food for clothing when utility is maximized? Show this graphically and algebraically.
g) Does Ann have a diminishing marginal rate of substitution of food for clothing? Show this graphically and algebraically.