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# Firm Profit Maximization

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I have 3 short Micro problems that I need some help with. Please provide detailed explanations.

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Hi, see the attached file. thanks.

Problem Set 7

***Explain all your work***

1) Firm Profit Maximization 1
Consider the market for textiles in the United States, which we will treat as perfectly competitive. The market demand for textiles is expressed as:
P = 250 - 0.5Q------------1
and the supply of textiles is expressed as:
P = Q/10--------------2
where P represents price per bolt of cloth and Q represents the number of bolts of cloth produced in the entire industry each day. The typical firm in this market has total cost
TC = 50 + 5q2--------------3
where q represents the number of bolts of cloth produced by a single firm each day. Thus, marginal cost is given by:
MC = 10q.---------------4

a) Determine the equilibrium market price and quantity in the market for textiles.

The equilibrium condition is when demand is equal to supply. Equating equation 1 and 2, we get,
250 -0.5Q = Q/10
Q=416.67
P=41.67
b) At the equilibrium market price computed in (a) above, what is the quantity produced by a typical firm?
The quantity produced by a typical firm will be when MR=MC
In perfect competition, MR=P=41.67
MC=10q=41.67, thus q=4.167

c) At the equilibrium market price computed in (a) above, what is the profit of a typical firm?
Profit of a typical firm: TR-TC
TR=P*q =41.67*4.167=173.62
TC=50+5*4.167^2=136.82
Profit = 173.62-136.82=36.8

d) If all firms in the market have the same cost structure, how many firms would compete at the equilibrium price computed in (a) above?
Q=The total quantity in the market = 416.67
q=4.167
No. of firms = Q/q = 416.67/4.167=100

e) If all firms in the ...

#### Solution Summary

Firm Profit Maximization is illustrated.

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