Question

Imagine there are two goods, H and S. The utility function is: U = H¹/²S¹/². The price of H is $6 and the price of S is $3. The budget is $18. What is the optimal quantity of H to consume?

Answer 1

To find the optimal quantity of H to consume, we need to maximize the utility function U = H¹/²S¹/² subject to the budget constraint. The optimal quantity of H to consume is 2.

Step-by-step explanation:

To find the optimal quantity of H to consume, we need to maximize the utility function U = H¹/²S¹/² subject to the budget constraint. Let's assume the quantity of H is x and the quantity of S is y. From the utility function, we can rewrite it as U = √(H) × √(S). To maximize U, we need to find the point (x, y) on the budget constraint where the ratio of marginal utility to price for H matches the ratio of marginal utility to price for S.

The budget constraint equation is 6x + 3y = 18. We can rearrange it as 2x + y = 6.

Using the utility function, we can calculate the marginal utilities of H and S. The marginal utility of H is (1/2)√(S)/√(H) and the marginal utility of S is (1/2)√(H)/√(S). Equating the ratios, we get (√(S)/√(H)) / (2/6) = (√(H)/√(S)) / (1/3). Solving for H, we find that the optimal quantity of H to consume is 2.