In class we considered TC(q) = q^2 + 4. AFC(q) is always decreasing, and AVC(q) is always increasing. Thus, two forces affect average cost: AC(q) = AVC(q) + AFC(q). Is it true that AVC(q) = AFC(q) at the minimum of AC(q) (the two "balance each other")? either prove the result for an arbitrary TC(q) function, or find a counterexample.
AC = TC/q = q + 4/q
Min AC means derivating AC with respect to q and putting it equal to 0.
Thus,
1 - 4/q2 = 0
This makes q = 2
Now,
AFC = 4/q = 4/2 = 2
AVC = q2/q = q = 2
Thus, it is true that at minimum of AC, AVC = AFC
In class we considered TC(q) = q^2 + 4. AFC(q) is always decreasing, and AVC(q) is...
In class we considered TC(q) = q^2 + 4. AFC(q) is always decreasing, and AVC(q) is always increasing. Thus, two forces affect average cost: AC(q) = AVC(q) + AFC(q). Is it true that AVC(q) = AFC(q) at the minimum of AC(q) (the two "balance each other")? either prove the result for an arbitrary TC(q) function, or find a counterexample.
Suppose that the cost function of a firm is C(Q) = 490 + 10Q^2 . (a) Provide the mathematical expressions for AFC, AVC, AC and MC. (b) Graph all the costs above as a function of Q. (c) What is true about the relation between the marginal cost and the average costs when the latter are at their minimum? And when the average cost are increasing (decreasing)? Explain.
Labor TVC TC MC AFC AVC ATC 25 50 75 100 25 125 (a) Complete the blank columns (5 points). Please create a table like mine and fill it. (b) Assume the price of this product equals $10. What's the profit-maximizing output (q)? (3 points). Note: managers maximize profits by setting MR=MC and under perfectly competitive markets, MR=Price. Thus, maximize profit by producing a where P=MC.(2 points) (c) What is the profit? (3 points) TOTAL COST (TC) - the...
Let the production function be as follow: 2. L0.7 K.3 q(L, K) Also assume w 2 and r=4 Find out if we have increasing, decreasing or constant return to scale. a. Derive the long-run cost function. TC(q) b. Derive the average cost curve. Is it increasing or decreasing or constant in q? С. Let the production function be as follow: 3. q(L, K) LK3 Also assume w-4 and r=3 Find out if we have increasing, decreasing or constant return to...
2. (54 points) Short-run costs. Suppose w 1, r 10 and K 20. C )q3 +200 a) (5 points) We have TC = WG) q3 + rK = On one graph (with q on the horizontal axis), graph the Total Cost, Variable Cost, and Fixed Cost functions. Pay attention to the shape of the curves, where they intercept the axes and each other (if they do), and the position of the curves relative to each other b) (9 points) Using...
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A firm's average fixed cost (AFC) is 10 when it produces Q=2. Then at Q=5, AFC is ... ОА. 8 Ов. 2 ос. 20 In a perfectly competitive market, the demand for a single firm's product is always O A. perfectly inelastic. O B. exactly as elastic as the market demand curve. O C. inelastic, but not perfectly inelastic. O D. perfectly elastic. As a firm's output increases: O A. average variable cost...
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TC AFC AVC ATC MC 40 60 20 lo 25 2 40 30 15 to 10 125 ms S 10 12.5 14 110 140 60 100.2 20 25. Но 25.7 3.9 179.9 5.7 111. 23115 24.9 2.0 9 300 334.3 44333 31.7 9q.4 10 40 HU0530 4uo.7 99. a. Fill out the table b. Assume the cost table is of the purely (perfectly) competitive firm. Price $40. What is the equilibrium quantity at that price. c. How much...
You have collected the following data on output and total variable costs: Q TVC ($) 10 72,800 20 124,400 30 159,600 40 183,200 50 200,000 60 214,800 70 232,400 80 257,600 90 295,200 100 350,000 Identify the range of output exhibiting increasing returns (increasing MP), and the range exhibiting diminishing returns (decreasing MP). Current fixed costs for the company equal $207,500. Draw two graphs, both with Q on the horizontal axis: one graph shows TVC and TC, and the other...
You have collected the following data on output and total variable costs Q TVC ($) 10 72,800 20 124,400 30 159,600 40 183,200 50 200,000 60 214,800 70 232,400 80 257,600 90 295,200 100 350,000 a. Identify the range LF output exhibiting increasing returns (increasing MP), and the range exhibiting diminishing returns (decreasing MP). b. Current fixed costs for the company equal $207,500. Draw two graphs, both with Q on the horizontal axis: one graph shows TVC and TC, and...
7. Assume that the long-run production function can be expressed as Q-SKL? Where Q is quantity of output, K is the quantity of capital and L is the quantity of labor. If capital is fixed at 10 units in the short run then the short-run production function is: Q=10KL b. Q=50KL? Q=10L? d. 0=50L Q=500KL 8. For a linear total cost function: a. MC will be downward sloping b. MC = AVC c. AVC is upward sloping and linear d....