Economics 2150A/B Lecture Notes - Form 10-Q, Average Variable Cost, Marginal Cost

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19 Apr 2014

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8. 7 a firm"s long-run total cost curve is tc (q)=1000 q corresponding long-run average cost curve, ac (q ). The equation of the ac curve is ac(q) = tc(q)/q = 1000q1/2/q = 1000q-(1/2). Given the relationship between ac and mc curves, the fact that the. Ac curve is decreasing means that the mc curve must lie below the ac curve. A firm"s long-run total cost curve is tc(q) = 40q 10q2 + q3, and its long-run marginal cost curve is mc(q) = 40 20q + 3q2. From the total cost curve, we can derive the average cost curve, The minimum point of the ac curve will be the point at which it intersects the marginal cost curve, 2 i. e. this implies that ac is minimized when q = 5. By definition, there are economies of scale when the ac curve is decreasing (i. e. q < 5) and diseconomies when it is rising (q > 5).

Related Questions

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?

salmonhyena380

Suppose that each firm in a competitive industry has the following costs:

Total Cost: TC=50+1/2 q2

Marginal Cost: MC=q

where q is an individual firm's quantity produced.

The market demand curve for this product is:

Demand QD=140-2P

where P is the price and Q is the total quantity of the good.

Each firm's fixed cost is $__________

What is each firm's variable cost?

_______ 50+1/2q

_______1/2q

_______q

_______1/2q2

Which of the following represents the equation for each firm's average total cost?

_____ 50/q

_______ 50/q+1/2q

_______1/2q

_______50+1/2q

Complete the following table by computing the marginal cost and average total cost for from 5 to 15.

5
6
7
8
9
10
11
12
13
14
15

The average total cost is at its minimum when the quantity each firm produces (q) iquals ________

Which of the following represents the equation for each firm's supply curve in the short run?

_______1/2q2

______q

_____50-q

_____120-1/2q2

In the long run, the firm will remain in the market and produce if________

Currently, there are 8 firms in the market.

In the short run, in which the number of firms is fixed, the equilibrium price is__________ In the short run, in which the number of firms is fixed, the equilibrium price is

________units. Each firm produces ________ nits. (Hint: Total supply in the market equals the number of firms times the quantity supplied by each firm.)

In this equilibrium, each firm makes a profit of _______ . (Note: Enter a negative number if the firm is incurring a loss.)

Firms have an incentive to EXIT/ENTER the market.

In the long run, with free entry and exit, the equilibrium price is _______and the total quantity produced in the market is__________units. There are ________

firms in the market, with each firm producing _________units.

orchidbadger835

1) Suppose that the demand curve faced by a particular firm is given by q = 300 - 5P. Could this be a perfectly competitive firm?

2) The market for wall clocks is perfectly competitive, and the current market price of a wall clock is $24. A particular firm has a short-run marginal cost of production of MC = 0.75q, where q is the number of clocks that it produces.

a. If it is optimal for the firm to produce a positive amount of output in the short run, how much should it produce?

b. Suppose that the firm has fixed costs of $3,000, and its average variable cost when producing the number of clocks found in part (a) is $20. Should the firm produce the amount that you found in part (a) or shut down (produce q = 0)?

c. Suppose instead (for this and all subsequent questions) that the firm has fixed costs of $240, and its variable cost when producing the number of clocks found in part (a) is $400. What is the firm's profit if it produces this amount of output?

d. Under the conditions described in part (c), if this is a constant-cost industry and the demand curve does not change over time, will firm enter this market in the long run or will firms exit this market in the long run?

goldyellowjacket576

Economics 2150A/B Lecture Notes - Form 10-Q, Average Variable Cost, Marginal Cost

ECON 2150A/B Full Course Notes

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