The Poster Bed Company believes tht its industry can best be classified as monop
ID: 1219695 • Letter: T
Question
The Poster Bed Company believes tht its industry can best be classified as monopolistically competitive. An analysis of the demand for its canopy bed has resulted in the following estimated demand function for the bed:
P= 1760-12Q
The cost analysis department has estimated the total cost function for the poster bed as
TC=1/3 Q3 - 15Q2 + 5Q+24,000
a. Calculate the level of output that should be produced to maximize short-run profits
b. What price should be charged?
c. Compute total profits at this price- output level?
d. Compute the point price elasticity of demand at the profit maxmizing level of output
e. What level of fixed costs is the firm experiencing on its bed production?
f. What is the impact of a $5000 increase in the level of fixed costs on the price charged, output produced, and profit generated?
Explanation / Answer
a. TC = 1/3 Q3 - 15Q2 + 5Q + 24,000
MC = Q2 - 30Q + 5
P = 1760 - 12Q
TR = 1760Q - 12Q2
MR = 1760 - 24Q
MC = MR
Q2 - 30Q + 5 = 1760 - 24Q
Q2 - 6Q - 1755 = 0
(Q - 45)(Q + 39) = 0
Q* = 45 units
b. P* = 1760 - 12(45) = $1,220
c. p = TR - TC
p = 1220(45) - [(1/3)(45)3 - 15(45)2 + 5(45) + 24,000]
p* = $30,675
d. P = 1760 - 12Q
Q = 1760/12 - P/12
dQ/dP = -1/12
ED = -1/12(1220/45) = -2.26
e. $24,000
f. Price and output remain the same, but profit declines by $5,000.
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