Question

How can I solve this problem? Can you please show step by step how to solve this?

Q^d = 2,000 − 10P

MC = 0.1Q

Answer 1

As no condition is provided in question whether market is perfectly competitive or Monopolistic we have worked out both possibilities

Part 1) when market is Perfectly competitive

Part 2) when market is  Monopolistic

Part 1)

In Ideal situation when we concern about Perfectly competitive firm then profit maximizing condition equals to

Price equals to Marginal Cost

In given question Q=2000-10*P

We can write above equation as

2000-Q=10*P

(2000-Q)/10=P

200-0.1*Q=P

This is called Inverse demand function

Now we are ready to find profit maximising output, Profit maximising Price and Maximum profit

P=MC=0.1Q

200-0.1Q=0.1Q
200=0.2Q

Q=1000 This is Profit maximizing quantity .. Price =200-0.1*Q=100 is Optimal Price when Market is perfectly competitive.

Part 2)

Hence Likewise you can solve for Price and Quantity for different markets such as Monopoly where Profit Maximizing condition is Price>MR=MC

You can find Revenue by Price * Quantity=(200-0.1*Q)Q=200*Q-0.1*Q^2

Marginal Revenue=200-0.2*Q
MC=0.1*Q

200-0.2Q=0.1Q

200=0.3*Q

Q=667 and Price=200-0.1(667)=133.33