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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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