# Equilibrium: Finding Profit Maximizing Output and Price

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.

https://brainmass.com/economics/general-equilibrium/equilibrium-finding-profit-maximizing-output-price-228595

#### 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.