Answer :
Let's solve each part of the question step-by-step using the provided data:
### Part a)
#### i) Average cost of producing two units:
The total cost of producing two units is given as GHC 15,000. To find the average cost per unit, we divide the total cost by the number of units:
[tex]\[ \text{Average cost of producing two units} = \frac{\text{Total cost for two units}}{\text{Number of units}} = \frac{15,000 \text{ GHC}}{2} = 7,500 \text{ GHC/unit} \][/tex]
#### ii) Total variable cost when output is five units:
To find the total variable cost when output is five units, we need to subtract the fixed cost from the total cost of producing five units. The fixed cost remains constant and is equal to the cost of producing zero units, which is GHC 10,000. The total cost for producing five units is GHC 40,000.
[tex]\[ \text{Total variable cost for five units} = \text{Total cost for five units} - \text{Fixed cost} = 40,000 \text{ GHC} - 10,000 \text{ GHC} = 30,000 \text{ GHC} \][/tex]
#### iii) Total average fixed cost of producing four units:
The fixed cost is GHC 10,000, and this remains constant regardless of the output level. To find the average fixed cost per unit for producing four units:
[tex]\[ \text{Average fixed cost for four units} = \frac{\text{Fixed cost}}{\text{Number of units}} = \frac{10,000 \text{ GHC}}{4} = 2,500 \text{ GHC/unit} \][/tex]
### Part b)
Given that the marginal cost of producing the sixth unit is GHC 20,000, we have to calculate the total cost of producing six units. The total cost of producing five units is GHC 40,000.
[tex]\[ \text{Total cost for six units} = \text{Total cost for five units} + \text{Marginal cost of the sixth unit} = 40,000 \text{ GHC} + 20,000 \text{ GHC} = 60,000 \text{ GHC} \][/tex]
### Part c)
To find the total profit of the firm when the output is six units, we first need to calculate the total revenue. The market price of the good is fixed at GHC 10,000 per unit. Therefore, the total revenue for six units is:
[tex]\[ \text{Total revenue for six units} = \text{Price per unit} \times \text{Number of units} = 10,000 \text{ GHC/unit} \times 6 = 60,000 \text{ GHC} \][/tex]
The total profit is then calculated as the total revenue minus the total cost:
[tex]\[ \text{Total profit for six units} = \text{Total revenue for six units} - \text{Total cost for six units} = 60,000 \text{ GHC} - 60,000 \text{ GHC} = 0 \text{ GHC} \][/tex]
### Part d)
In what market is the firm selling? Explain your answer.
The firm is selling in a perfectly competitive market. This is indicated by the fact that the price of the good is fixed and does not change with the level of output. In a perfectly competitive market, firms are price takers, meaning they accept the market price and cannot influence it. The given price of GHC 10,000 per unit being constant regardless of the quantity supplied is a characteristic feature of perfect competition.
### Part a)
#### i) Average cost of producing two units:
The total cost of producing two units is given as GHC 15,000. To find the average cost per unit, we divide the total cost by the number of units:
[tex]\[ \text{Average cost of producing two units} = \frac{\text{Total cost for two units}}{\text{Number of units}} = \frac{15,000 \text{ GHC}}{2} = 7,500 \text{ GHC/unit} \][/tex]
#### ii) Total variable cost when output is five units:
To find the total variable cost when output is five units, we need to subtract the fixed cost from the total cost of producing five units. The fixed cost remains constant and is equal to the cost of producing zero units, which is GHC 10,000. The total cost for producing five units is GHC 40,000.
[tex]\[ \text{Total variable cost for five units} = \text{Total cost for five units} - \text{Fixed cost} = 40,000 \text{ GHC} - 10,000 \text{ GHC} = 30,000 \text{ GHC} \][/tex]
#### iii) Total average fixed cost of producing four units:
The fixed cost is GHC 10,000, and this remains constant regardless of the output level. To find the average fixed cost per unit for producing four units:
[tex]\[ \text{Average fixed cost for four units} = \frac{\text{Fixed cost}}{\text{Number of units}} = \frac{10,000 \text{ GHC}}{4} = 2,500 \text{ GHC/unit} \][/tex]
### Part b)
Given that the marginal cost of producing the sixth unit is GHC 20,000, we have to calculate the total cost of producing six units. The total cost of producing five units is GHC 40,000.
[tex]\[ \text{Total cost for six units} = \text{Total cost for five units} + \text{Marginal cost of the sixth unit} = 40,000 \text{ GHC} + 20,000 \text{ GHC} = 60,000 \text{ GHC} \][/tex]
### Part c)
To find the total profit of the firm when the output is six units, we first need to calculate the total revenue. The market price of the good is fixed at GHC 10,000 per unit. Therefore, the total revenue for six units is:
[tex]\[ \text{Total revenue for six units} = \text{Price per unit} \times \text{Number of units} = 10,000 \text{ GHC/unit} \times 6 = 60,000 \text{ GHC} \][/tex]
The total profit is then calculated as the total revenue minus the total cost:
[tex]\[ \text{Total profit for six units} = \text{Total revenue for six units} - \text{Total cost for six units} = 60,000 \text{ GHC} - 60,000 \text{ GHC} = 0 \text{ GHC} \][/tex]
### Part d)
In what market is the firm selling? Explain your answer.
The firm is selling in a perfectly competitive market. This is indicated by the fact that the price of the good is fixed and does not change with the level of output. In a perfectly competitive market, firms are price takers, meaning they accept the market price and cannot influence it. The given price of GHC 10,000 per unit being constant regardless of the quantity supplied is a characteristic feature of perfect competition.
