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Microeconomics Perfect Competition Problems - Each firm L/R Avg Cost minimized at qi = 20 units @$10/unit QD = 1500 - 5P.

(a) What is L/R supply?

Answer - The long run supply curve is as follows: p=$10.

(b) What is L/R equilibrium price?

The long run equilibrium price is the minimum average total cost which is $10 and the quantity is as follows:

Q = 1500 - (5*10) = 1450

The equilibrium output of the firm is the minimum average cost which is 20 units. The number of firms is as follows:

Number of firms = 1450/20 = 72.5 or 73 firms

The profit of each firm is normal profit or zero profit as the firm is in equilibrium.

(c) Calculate SRAC + SMC function.

Short run average total cost is as follows:

SRAC = (0.5q2-10q+200)/q = 0.5q-10 + 200/q

The short run marginal cost is as follows:

SMC = dC/dq = q-10

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(d) Calculate S/R supply function eq. firm and industry total.

The supply curve of the firm is the marginal cost which is: p = q-10

The industry supply curve is as follows: p = 73q-730

(e) Change in demand QD = 2000 - 50P. Answer "b" again in S/R when output can't change.

The long run equilibrium price is same as before which is $10, the firm output is 20 units, the quantity equilibrium is: Q = 2000 - (50*10) = 1500 units

The number of firms is: Firms = 1500/20 = 75

(f) In S/R, use industry S/R supply to recalculate (b).

The long run equilibrium is where the total revenue is equal to total cost as the firms earn zero profits:

2000p - 50p2 = (p+730)/73*p

146000p-3650p2 = p2 + 730p

145270p - 3651p2 = 0

p = 145270/3651 = 39.78 or $39

(g) What is new L/R equilibrium?

The new long run equilibrium is where minimum of average cost curve:

min of SRAC = 0.5 - 200/q2

0.5 - 200/q2 = q-10

10.5 - q - 200/q2 = 0

10.5q2 - 1/q - 200 = 0

(h) What id profit function + supply function.

The supply function is the rising part of marginal cost:

MC = (dCT(p, w))/dq

The profit function is as follows: profit = total revenue - total cost = p*q(p,w) - CT(p,w).

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