Let's solve this step-by-step, starting with the given information:

Given Data:

• Production function: $y = k^{\frac{2}{3}} l^{\frac{1}{3}}$
• Capital cost per unit: $1,920 (with one unit of capital)
• Wage rate per hour: $15
• Labor employed: 8 hours
• Capital employed: 1 unit

Part A: Calculating Total Cost

Since you cannot change the capital and you are employing 8 hours of labor, the total cost $C$ consists of the fixed cost of capital and the variable cost of labor.

1. Fixed Cost (Capital Cost): $\text{Fixed Cost} = \text{Capital Cost} = 1 \times 1920 = 1920$

2. Variable Cost (Labor Cost): $\text{Variable Cost} = \text{Wage Rate} \times \text{Labor Hours} = 15 \times 8 = 120$

3. Total Cost: $C = \text{Fixed Cost} + \text{Variable Cost} = 1920 + 120 = 2040$

Part B: Calculating Average Cost

The Average Cost (AC) is the total cost divided by the total production, $y$.

To find $y$, we use the production function: $y = k^{\frac{2}{3}} l^{\frac{1}{3}}$ Given $k = 1$ and $l = 8$: $y = 1^{\frac{2}{3}} \cdot 8^{\frac{1}{3}}$ Since $1^{\frac{2}{3}} = 1$, this simplifies to: $y = 8^{\frac{1}{3}} = 2$

Now we can calculate the Average Cost: $\text{AC} = \frac{C}{y} = \frac{2040}{2} = 1020$

Part C: Calculating Marginal Cost

The Marginal Cost (MC) can be found by taking the derivative of the total cost with respect to $y$. However, since we are given a production function that implies certain proportional relationships, we can approximate the marginal cost by determining the increase in cost with a small additional unit of output.

Given the setup here, if labor increases slightly, the additional cost per unit of output will approximate to the wage rate adjusted by production elasticity with respect to labor (which can be complex to specify directly here without calculus-based marginal cost). However, with only one unit of capital and a single step analysis, additional MC derivation requires advanced optimization setup.