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Equilibrium: Finding Profit Maximizing Output and Price

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Given the following Demand & Supply functions:
Qd = 25 – P
Qs = 10 + 2P
a – What is the equilibrium values of P and Q?

Now suppose the demand function changes to:
Qd = 10,000 – 2P

If Total Cost function is:
TC = 5000 + 50Q
b - Find the Profit – maximizing Quantity and Price.
c – Find the firm’s profit.

Given the following Demand and Cost functions for a monopolistically competitive firm:
Qd = 100,000 - 20P
TC = 1,000 + 10Q + .05Q to the power of 2

a. Find the profit maximizing Quantity and Price.
b. Find the Profit.

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Solution Preview

Solution is attached as word document also.

Soution 1.
a - What is the equilibrium values of P and Q?
For equilibrium
Qd=Qs
25-P=10+2P
3P=25-10=15
3P=15
P=15/3=5
Qd (at P=5) =25-5=20
Qs (at P=5) =10+2*5=10+10=20
Equilibrium Price =$5
Equilibrium Quantity=20

Now suppose the demand function changes to:
Qd = 10,000 - 2P
If Total Cost function is:
TC = 5000 + 50Q

b - Find the Profit - maximizing Quantity and ...

Solution Summary

There are two problems. Solutions to given problems explain the steps to find out equilibrium price and quantity. It also explains the steps to find out profit maximizing output and price.

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Finding optimum price and output levels..

Perfect Competition
Given the following equations:

Qd=-1000P+Income+11000
TC=(1/70)q^2-(25/35)q+100
MC=(1/35)q-(25/35)
Number of firms =85

Assume Income =11000.
i.What is the market supply equation?
ii.What is the market equilibrium price ?
iii.What is the market equilibrium quantity?
iv.What is the profit maximizing output (PMO) level?
v.What is the average profit and total profit at this PMO level?

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