Calculate the average fixed cost of 7 units of output.

1. Level of Output

Step 1: Identify the given values. Total Costs (TC) = $2400 Average Total Cost (ATC) =$20 per unit

Step 2: Use the formula for Average Total Cost to find the quantity (level of output). $\text{ATC} = \frac{\text{TC}}{\text{Q}}$ Rearrange to solve for Q: $\text{Q} = \frac{\text{TC}}{\text{ATC}}$

Step 3: Substitute the given values and calculate Q. $\text{Q} = \frac{\$2400}{\$20/\text{unit}}$ $\text{Q} = 120 \text{ units}$ The information about average variable cost ($15) is not needed to solve for the level of output using the given total cost and average total cost.

The level of output is $\boxed{\text{120 units}}$.

2. Condition for Equi-Marginal Utility

To maximize utility, a consumer will allocate their income such that the last dollar spent on each good yields the same amount of marginal utility. This is known as the Law of Equi-Marginal Utility.

The condition for equi-marginal utility for goods x, y, and z is: $\frac{\text{MU}_{\text{x}}}{\text{P}_{\text{x}}} = \frac{\text{MU}_{\text{y}}}{\text{P}_{\text{y}}} = \frac{\text{MU}_{\text{z}}}{\text{P}_{\text{z}}}$ Where $\text{MU}$ is the marginal utility of a good and $\text{P}$ is its price.

3. Unit Cost of Production

Step 1: Identify the given cost function and output level. Total Cost (TC) function: \text{TC} = \(20 + 10X)$ Level of output (X) = 10 units

Step 2: Calculate the Total Cost (TC) for X = 10 units. $\text{TC} = 20 + 10(10)$ $\text{TC} = 20 + 100$ $\text{TC} = \$120$

Step 3: Calculate the unit cost (Average Total Cost, ATC) by dividing Total Cost by the level of output. $\text{Unit Cost (ATC)} = \frac{\text{TC}}{\text{X}}$ $\text{Unit Cost (ATC)} = \frac{\$120}{10 \text{ units}}$ $\text{Unit Cost (ATC)} = \$12/\text{unit}$

The unit cost of producing 10 units of output is \boxed{\12/unit}$.

4. Average Fixed Cost for 7 Units of Output

Step 1: Determine the Fixed Cost (FC) from the given table. Fixed cost is the cost that does not change with the level of output. We can find it by subtracting the variable cost of the first unit from its total cost. At 1 unit of output: Total Cost (TC) = $60 Marginal Cost (MC) of the 1st unit =$53 The variable cost of the 1st unit (VC(1)) is equal to its marginal cost. $\text{VC}(1) = \text{MC}(1) = \$53$ Fixed Cost (FC) = Total Cost (TC) - Variable Cost (VC) $\text{FC} = \text{TC}(1) - \text{VC}(1)$ $\text{FC} = \$60 - \$53$ $\text{FC} = \$7$ (We can verify this with Q=2: TC(2)=100, MC(2)=40. VC(2) = VC(1) + MC(2) = 53+40=93. FC = TC(2) - VC(2) = 100-93=7. The fixed cost is consistently $7.)

Step 2: Calculate the Average Fixed Cost (AFC) for 7 units of output. $\text{AFC} = \frac{\text{FC}}{\text{Q}}$ $\text{AFC} = \frac{\$7}{7 \text{ units}}$ $\text{AFC} = \$1/\text{unit}$

The average fixed cost for 7 units of output is \boxed{\1/unit}$.