In the shortrun function of a company with a constant variable cost is given by the equation q=225+55q,where TC is the total cost and q is the total quantity of output,both measured in thousands.1.what is a company's fixed cost?2.if the company produced 100,000 units of goods,what would be its average variable cost? 3.what would be its marginal cost of production? 4.what would be its average fixed cost?
To find the answers, we need to understand the given equation and its components.
1. Fixed Cost:
In the short-run function equation, the term "225" represents fixed cost. Therefore, the fixed cost for the company is 225,000 (as the equation measures the cost in thousands).
2. Average Variable Cost (AVC):
The average variable cost can be derived by dividing the total variable cost by the quantity of output. In this case, the variable cost is determined as the difference between total cost (TC) and fixed cost (225,000). The formula for AVC is as follows:
AVC = (TC - Fixed Cost) / q
Using the given equation, we can substitute the values:
AVC = (225 + 55q - 225,000) / q
To find the AVC when the company produces 100,000 units (q = 100), we substitute q = 100 into the equation:
AVC = (225 + 55(100) - 225,000) / 100
AVC = (225 + 5500 - 225000) / 100
AVC = -219275 / 100
AVC = -2192.75
Therefore, the average variable cost would be -2192.75 dollars. Be aware that the negative sign may indicate an error in the calculation.
3. Marginal Cost of Production (MC):
The marginal cost represents the additional cost incurred when producing one more unit of output. In this case, the MC can be derived from the equation as the derivative of the total cost (TC) with respect to quantity (q). The formula for MC is as follows:
MC = dTC / dq
Using the given equation, we can find the derivative of TC with respect to q:
MC = d(225 + 55q) / dq
MC = 55
Regardless of the quantity produced, the marginal cost of production will always be 55.
4. Average Fixed Cost (AFC):
The average fixed cost can be derived by dividing the total fixed cost by the quantity of output. In this case, the total fixed cost is 225,000. The formula for AFC is as follows:
AFC = Fixed Cost / q
Using the given equation:
AFC = 225,000 / q
To find the AFC when the company produces 100,000 units (q = 100), we substitute q = 100 into the equation:
AFC = 225,000 / 100
AFC = 2,250
Therefore, the average fixed cost would be 2,250 dollars.
To find the answers to these questions, we need to understand the given equation: q = 225 + 55q.
1. To find the fixed cost of the company, we need to determine the value of q when there is zero output (q = 0). Plugging in q = 0 in the equation, we get: 0 = 225 + 55(0). Solving this equation, we find that the fixed cost of the company is $225,000 (in thousands).
2. To find the average variable cost, we need to divide the total variable cost (TVC) by the quantity of output (q). The total variable cost can be represented by the difference between the total cost (TC) and the fixed cost (FC). So, TVC = TC - FC. For the company to produce 100,000 units of goods, we can plug in q = 100 in the equation q = 225 + 55q. Solving for TC, we get: TC = 225 + 55(100) = 5,725. Now, calculating the TVC: TVC = TC - FC = 5,725 - 225 = 5,500. Finally, dividing the TVC by q (100), we find that the average variable cost is $55 (in thousands).
3. The marginal cost of production represents the change in total cost (TC) when there is a change in output by one unit. In this case, the marginal cost can be found by taking the derivative of the total cost function with respect to q. Differentiating the equation q = 225 + 55q, we get: dTC/dq = 55. Thus, the marginal cost of production is $55,000 (in thousands).
4. The average fixed cost can be found by dividing the fixed cost (FC) by the quantity of output (q). We already determined that the fixed cost is $225,000 (in thousands). Now, we need to find the value of q for which we want to calculate the average fixed cost. In this case, if the company produced 100,000 units of goods, we can plug in q = 100 in the equation q = 225 + 55q. Solving for FC, we get: FC = 225 + 55(100) = 5,725. Finally, dividing the FC by q (100), we find that the average fixed cost is $2,250 (in thousands).