Question

Mr. Sharma’s consumption preference for tea (denoted by \( x \)) and sugar (denoted by \( y \)) is given by the utility function \[ U(x,y) = \min(x, 2y) \] The price per unit of tea is 10 and the price per unit of sugar is 10. Mr. Sharma’s total income is 900. The optimum quantity of tea purchased by Mr. Sharma equals _________ (in integer).

Hint:

When maximizing utility subject to a budget constraint, substitute the relationship from the utility function into the budget equation to solve for the optimal quantities of goods.

Answer 1

Correct Answer: 60

The utility function is \( U(x,y) = \min(x, 2y) \). This implies that to maximize utility, we should set \( x = 2y \), i.e., the quantity of tea should be twice the quantity of sugar. Let \( x = 2y \), and since Mr. Sharma’s total income is 900, we have the budget constraint: \[ 10x + 10y = 900. \] Substitute \( x = 2y \) into the budget constraint: \[ 10(2y) + 10y = 900, \] \[ 20y + 10y = 900, \] \[ 30y = 900, \] \[ y = 30. \] Thus, \( x = 2y = 60 \). The optimum quantity of tea purchased by Mr. Sharma is 60.