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Suppose the cost function is C(Q) = 50 + Q- 10(Q) squared + @Q(cubed). What is the marginal cost of producing 10 units?

401? 1060? 560? or 1010?

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Related questions

Suppose the cost of producing q cars is given by c(q) = 7500 +2000q-10q^2

a. What is the variable cost of producing 10 cars?

b. What is the marginal cost of producing the 10th car?

c. Solve for AC(q) and AVC(q) and are they increasing?

An economist estimated that the cost function of a firm is:

C(Q) = 100 + 20Q + 15Q2 + 10Q3

And, MC(Q) = 20 + 30Q + 30Q2

Based on this information, determine:

1) The fixed cost of producing 10 units of output

2) The variable cost of producing 10 units of output

3) The total cost of producing 10 units of output

4) The average fixed cost of producing 10 units of output

5) The average variable cost of producing 10 units of output

6) The average total cost of producing 10 units of output

7) The marginal cost when Q = 10

3. A firm has a long-run production function:   

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run? 

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?

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