I have to do a simple managerial economics exercise.
I know that a firm sells $Q=16000$ units at a price of $P=1672$.
Moreover, I know that
- it will sell 18% more units if the firm decrease the price by 20%
- it will sell 10% less units if the firm increase the price by 5%
I need to find the linear price function $P(Q)$.
I guess I need to find the price function using my initial point $(Q,P)=(16000,1672)$ and the price elasticity in some point.
But from the information about how the number of units sold will change due to a change in price, I obtain two different price elasticities.
- elasticity1 = 18%/(-20%) = -0.9
- elasticity2 = -10%/5% = -2
Am I doing it correctly?
I'm really not sure if I'm doing it correctly, because to me it seems that I can simply get 3 points $(Q1,P1)=(16000,1672)$, $(Q2,P2)=(16000 \cdot 1.18,1672 \cdot 0.8)$, and $(Q3,P3)=(16000 \cdot 0.9,1672 \cdot 1.05)$. But using these 3 points, the price function is not linear, so I guess I need to do something else.