Question

1. A student has an income of $100 and buys only 2 goods: pizza and books. A pizza costs $2 a slice and books cost $10 each. At the student’s present level of consumption, his marginal utility of pizza is 4 and his marginal utility of books is 2.

1. At the current level of consumption, is the student maximizing his level of utility given his budget constraint?

   b. Draw a graph showing his current consumption point using indifference curves and the budget constraint.

Answer 1

1. Income M = 100 , Price of pizza P_X = $2 per slice , Price of book P_Y = $10 , Marginal utility of pizza MU_X = 4 and Marginal utility of book MU_Y = 2.

For maximization of utility , MU_X / MU_Y = P_X / P_Y

But, 4/2 > 2/10

Hence, his utility is not maximum.

2. Budget constraint can be written as M = XP_X + YP_Y or, 100 = 2X + 10Y where X and Y are quantity of pizza and books respectively.

If he only buys X , quantity of X = income / price of X = 100/2 = 50

and if he only buys Y, quantity of Y = income/price of Y = 100/10 = 10

Indifference curves are drawn below.

As MU_X/MU_Y > P_X/P_Y , there will be corner solution towards X(Pizza).

Current consumption is at point e where number of pizza slices = 25 and number of books = 10 . However, utility is not maximum at point e. Utility is higher at point f.