Final answer:
In equilibrium, Daniel will purchase approximately 0.5 units of A, 0.333 units of B, and 1 unit of C based on the given prices of $2 for A, $3 for B, and $1 for C.
Step-by-step explanation:
In equilibrium, the quantity of each item purchased will depend on various factors, including their prices. To determine how much of each item Daniel will purchase, we need to consider the relative prices and preferences. One way to analyze this is through the concept of marginal utility. Marginal utility measures the additional satisfaction or benefit gained from consuming one more unit of a good or service.
Let's assume that Daniel's preferences can be represented by a utility function, where U(A, B, C) represents his total utility from consuming goods A, B, and C. Assuming that prices do not change, Daniel will allocate his budget in such a way that the marginal utility per dollar spent is equal for each good. This means that the ratio of the marginal utility to the price should be the same for all goods.
For example, let's say Daniel's utility function is U(A, B, C) = A + B + C. The marginal utility of A, denoted as MU(A), represents the additional benefit from consuming one more unit of good A. Similarly, MU(B) and MU(C) represent the marginal utilities of B and C, respectively. The prices are given as follows: P(A) = $2, P(B) = $3, and P(C) = $1.
Daniel will purchase each good until MU(A)/P(A) = MU(B)/P(B) = MU(C)/P(C). Let's calculate the marginal utilities:
- MU(A) = 1
- MU(B) = 1
- MU(C) = 1
Now, we can calculate the quantities of goods Daniel will purchase:
- Quantity of A = MU(A)/P(A) = 1/2 = 0.5
- Quantity of B = MU(B)/P(B) = 1/3 = 0.333 (rounded to 3 decimal places)
- Quantity of C = MU(C)/P(C) = 1/1 = 1
Therefore, in equilibrium, Daniel will purchase approximately 0.5 units of A, 0.333 units of B, and 1 unit of C. Keep in mind that these quantities may vary depending on the specific utility function and prices.