Short-Run Economic Costs Suppose a firm has a short-run cost equation of C(q) =

Question

Short-Run Economic Costs Suppose a firm has a short-run cost equation of C(q) = 0.3q3 – 15q2 + 200q + 100, and short-run marginal cost equation of MC(q) = 0.9q2 – 30q + 200, if the firm produces 25 units of output: a. Solve for total fixed cost, total variable cost and total cost. (3 points) b. Solve for the firm’s average fixed cost, average variable cost and average total cost. (3 points) c. Use the MC(q) equation to solve for the marginal cost of the last unit produced. (2 points) d. Solve for whether the firm has short-run economies of scale or diseconomies of scale. (2 points)

Explanation / Answer

C(q) = 0.3q3 – 15q2 + 200q + 100

MC(q) = 0.9q2 – 30q + 200

If the firm produces 25 units of output;

A) TFC is independent of quantity of production and remains same throughout. It is equal to 100 as given in cost equation.

TVC(q) = 0.3q3 – 15q2 + 200q; Putting q = 25

0.3(25)3 – 15(25)2 + 200(25) => 4687.5 - 9375 + 5000 => 312.5

TC = TVC + TFC => 312.5 + 100 => 412.5

B) AFC = TFC/Q => 100 / 25 => 4

AVC = TVC/Q => 312.5 /25 => 12.5

ATC = TC/Q => 412.5 /25 => 16.5

C) MC(q) = 0.9 (25) 2 – 30 (25) + 200

   = 562.5 - 750 + 200 => 12.5

D) AVC is same as MC, which happens when AVC is minimum. Average Cost curves are U shaped. Initially cost decreases with increase in production, reaches minimum and then increases with increase in production.

So firm is experiencing economies of scale.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.