What is marginal cost equal to when Q = 10?

To find the total cost of producing 20 units of output given the marginal cost function \( MC = \frac{10}{Q} \) and the total cost is 500 when \( Q = 10 \), follow these steps: 1. **Understand the relationship between total cost and marginal cost**: The total cost \( TC \) can be found by integrating the marginal cost \( MC \) and adding the fixed cost \( C \). 2. **Set up the integral for total cost**: \[ TC(Q) = \int MC \, dQ + C \] Given \( MC = \frac{10}{Q} \), we have: \[ TC(Q) = \int \frac{10}{Q} \, dQ + C \] 3. **Find the antiderivative**: \[ \int \frac{10}{Q} \, dQ = 10 \ln|Q| + C \] So, \[ TC(Q) = 10 \ln|Q| + C \] 4. **Use the given information to find the constant \( C \)**: Given that \( TC(10) = 500 \): \[ 500 = 10 \ln(10) + C \] \[ C = 500 - 10 \ln(10) \] 5. **Find the total cost for \( Q = 20 \)**: \[ TC(20) = 10 \ln(20) + C \] Substitute \( C \): \[ TC(20) = 10 \ln(20) + 500 - 10 \ln(10) \] Simplify: \[ TC(20) = 10 (\ln(20) - \ln(10)) + 500 \] \[ TC(20) = 10 \ln\left(\frac{20}{10}\right) + 500 \] \[ TC(20) = 10 \ln(2) + 500 \] 6. **Calculate the numerical value**: \[ \ln(2) \approx 0.6931 \] \[ TC(20) = 10 \times 0.6931 + 500 \] \[ TC(20) = 6.931 + 500 \] \[ TC(20) \approx 506.93 \] So, the total cost of producing 20 units of output is approximately \( 506.93 \). The correct answer is: - \( 506.93 \)

When price equals marginal cost

The total cost of producing a certain good is given by TC=300ln(q+30)+150. Find the marginal cost (MC) and the avarage cost (AC) functions.

Suppose there are 100 firms each with a short run total cost of STC = q2 + q + 10, so that marginal cost is MC = 2q +1. If market demand is given by QD = 1050 - 50P, profit to the firm will beQuestion 3Select one:a.5.b.6.c.15.d.9.

Refer to Scenario 15.5. Suppose there are 100 firms each with a short run total cost of TC = q2 + q + 4, so that marginal cost is MC = 2q +1. If market demand is given by QD = 1050 − 50P, how much will be produced in the market ( Call this Q)?  and what profit will each firm make?Group of answer choicesQ=300, Profit = $25Q=400, Profit = $15Q=500, Profit = $21Q=600, Profit = $50