Question

Question (5): A consumer who has a utility function modeled as U(x,y) = min (5x, 10y) is faced with the prices of $2 and $6 per unit of x and y respectively. The consumer will spend his/her entire disposable income of $30. How many units of x and y will the consumer consume that will provide the maximum utility?! (a) 6 units of x and 3 units of y. (b) 3 units of x and 6 units of y. (c) 5 units of x and 10 units of y. (d) 10 units of x and 5 units of y. (e) None of the above. Answer:

Answer 1

Answer 5

Maximize : U = min{5x,10y)

subject to : 2x + 6y = 30----------Budget constraint

We can see from above utility function that he considers x and y as perfect complements. In order to maximize for such a function a firm produces at a point where Budget line intersects kink point of indifference curve.

Here Kink will occur when we have 5x = 10y => x= 2y

Putting this in Budget constraint we get :

2(2y) + 6y = 30 => y = 3 and x = 2y = 2*3 = 6 => x = 6

Hence, the correct answer is (a) 6 units of x and 3 units of y.