A firm produces x tonnes of output at a total cost of C(x)=1/10x^3-4x^3+20x+5.
1. Find the avaerage cost
2. Average variable cost
3. Average fixed cost
4. Marginal Cost
5. Marginal average cost
To find the average cost, we need to divide the total cost by the quantity of output.
1. Average cost is given by C(x)/x:
Average cost = (1/10x^3 - 4x^2 + 20x + 5)/x
To find the average variable cost, we need to subtract the average fixed cost from the average cost. The average fixed cost is the fixed cost divided by the quantity of output.
2. Average variable cost = Average cost - Average fixed cost
To find the average fixed cost, we need to find the fixed cost, which is the cost when x = 0.
3. Fixed cost = C(0) = 1/10(0)^3 - 4(0)^2 + 20(0) + 5 = 5
Average fixed cost = Fixed cost/x
To find the marginal cost, we need to find the derivative of the total cost function with respect to x.
4. Marginal cost = dC(x)/dx
To find the marginal average cost, we need to find the derivative of the average cost function with respect to x.
5. Marginal average cost = d(Average cost)/dx