Question

find MR , TR ,Q*, P*

1. Q= 25-2p

2. P = 100-10Q

3. 50- 0.5 P

4. 10-0.1Q

Answer 1

Finding MR for $Q = 25-2P$

$Q= 25-2P$

$TR = QP = (25-2P)P$

$=25P -2P^2$

$MR =\frac{\Delta TR}{P} = 25-4P$

2. P = 100-10Q

$TR = PQ = (100- 10Q)Q$

$= 100Q-10Q^2$

$MR =\frac{\Delta TR}{Q} = 100-20Q$

3. 50- 0.5 P

Finding $P^*$ We assume Q = 0

$0 = 50 - 0.5P$

$P^* = \frac{50}{0.5} = 100$

4.10-0.1Q

Finding $Q*$ we assume P = 0

$0 = 10-0.1Q$

$P^* = \frac{10}{0.1} = 100$