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A competitive firm has estimated its average variable cost function as:

AVC = 20 - 0.04Q + 0.00005Q2

Total fixed cost is $500

a. The marginal cost function associated with this AVC function is SMC = _____.
b. AVC reaches its minimum at _____ units of output at which AVC = _____. The forecasted price is P = $23.60.
c. To maximize its profit, the firm should produce _____ units of output. Profit (loss) is _____.
Suppose the forecasted price is P = $10.
d. The firm should produce _____ units of output for a profit (loss) of $_____.

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Joshua Stredder
Joshua StredderLv10
28 Sep 2019

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Related questions

1. The manager of a monopoly firm obtained the following estimate of the demand for its product.

Q = 1000 - 100P + 0.2M - 500PR

where M and PR are, respectively, consumer income and the price of a related good. The forecasted values for M and PR are M = $30,000 and PR = $5.

a. What is the forecasted demand function? ((Show work))

b. What is the inverse demand function? (Show work)

c. What is the marginal revenue function? (Show work)

The estimated average variable cost is

AVC = 40 - 0.08Q + 0.0001Q2

d. To maximize profit the firm should produce ______ units of output.

e. To maximize profit the firm should set a price of ______

f. Check to see if the firm should produce in the short run rather than shut down.

g. Total fixed cost is $5,000. The firm makes a profit (loss) of _____.

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form and obtained the following results. Total fixed cost (TFC) at Straker Industries is $820.

Adjusted R Square 0.710

Dependent variable = AVC

Coefficients Standard Error t Stat P-value

Intercept 41.80 4.04 10.35 0.000

Q -2.34 0.89 -2.64 0.017

Q^2 0.17 0.04 4.15 0.001

a. What level of output (Q) is associated with the minimum AVC? What is the value of AVC at this minimum?

b. Determine equations for ATC, TC, and SMC. Graph one scatterplot of Q vs. TC, and another scatterplot of Q vs. ATC, AVC, and SMC.

c. When output is 16, how much is TC, AVC, ATC, and SMC?

d. At what amount of output does labor change from exhibiting increasing returns to decreasing returns?

I believe I have figured out a-c, but I cannot get d.

I found that p=3

2.

Consider a perfectly competitive firm that faces the following market demand and market supply curves:

Demand : Qd = 10,000 -10,000P + 2M

Supply: Qs =40,000 +10,000P -4,000Pi

M=25,000 and Pi=10

The firm has also estimated its AVC function to be equal to :

AVC = 3.0 -.0027Q +.0000009Q2

And Fixed Costs =1600.

a. Find the profit maximizing output for this firm. What are profits?

b. Suppose demand shifts down and the new market price is $1.50. What is the profit maximizing output at this price? What are profits in this case?

c. Given your result in part b, should this firm produce or shut down? Graph the result in part b, assuming the price of $1.50, and label your SRMC, AVC and SRATC curves. Justify your answer graphically and numerically.

d. How far can market price fall before the profit maximizing perfectly competitive firm should shut down?

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