Question

Sophie has $ 76, the price of gasoline is $4 per gallon and the price of food is $20 per meal. Use the information in the following table to analyze her choice.

Gas	Marginal Utility of Gas	Marginal Utility of Gas over the price of Gas	Food	Marginal Utility of Food	Marginal Utility of Food over the price of Food
1	120		1	600
2	116		2	560
3	112		3	500
4	100		4	460
5	92		5	360
6	80		6	320

What is the best combination of food and gasoline that maximizes her utility?

		4 units of Gas and 3 units of food
		4 units of Gas and 4 units of food
		5 units of Gas and 3 units of food
		5 units of Gas and 5 units of food

Answer 1

Optimal is attained where MUx/Px = MUy/Py and Px.X + Py.Y = Income

4X + 20Y = 76

X is the units of Gas

Y is the units of Food

Combination of output where MUgas/Pgas = MUfood/Pfood are (1 Gas; 1 Food), (3 Gas; 2 Food), (4 Gas, 3 Food), (5 Gas, 4 Food)

Cost of (1 Gas; 1 Food) = 4 x 1 + 20 x 1 = 4 + 20 = 24 < 76

Cost of (3 Gas; 2 Food) = 4 x 3 + 20 x 2 = 12 + 40 = 52 < 76

Cost of (4 Gas; 3 Food) = 4 x 4 + 20 x 3 = 16 + 60 = 76 = Income

Answer is; 4 units of Gas and 3 units of food