Answer to Question #235529 in Microeconomics for Johdrick

Question

Felina prefers to spend her living allowance of $1500 on Mobile data and food. She prefers to pay purchase $10 Mobile Data (D) per week and spend $50 on food expenditure (F). Her utility function with the given income, prices of the two goods and preferences is as follows: U(D,F) = 4 D 3/4 F 1/4 a. What utility-maximizing combinations of mobile data and food should Felina buy in a semester with the given income and prices of the two goods? 

Answer 1

The indifference curve would be tangent to the budget line which would result in the equilibrium condition as a result the MRS would be equal to the price ratio. The utility maximisation problem would result in maximisation of the utility given the prices and income.

The utility would be maximised when the budget would remain same. The utility would maximise when the budget and prices would remain same.

$FD=\frac{\$50}{\$10}\\FD=\$5\\F=5D$

$10D+50F=1500\\10D+250D=1500\\260D=1500\\D=\frac{1500}{260}\\\frac{150}{26}\\=5.76$

$10F+50(5.76)=1500\\10F=1500-288\\10F=1212\\F=121.2$

The utility maximising bundle would result in the (F,D) which is (121.2,5.76) given the income and the prices remain same.