Vito is the sole producer of skateboards in Perisher. The inverse demand for skate boards according to Vito is:
P = 100 - S
where S and P respectively denote output and price of skateboard. Marginal cost of producing a skateboard is $20.
(a) Find the level of S that maximizes Vito's profit. Also, find the equilibrium price, and the equilibrium level of profit
Vito's brother Pedro thinks that Vito has got it wrong. According to Pedro, the inverse demand function for skateboards in Perisher is actually the following:
P = 200 - 4S
(b) Assume Pedro is right. Find the level of S that maximizes profit. Also, find the equilibrium price, and the equilibrium level of profit.
To resolve their differences Vito and Pedro hired a marketing consultant. It turned out that the inverse demand for skateboards in Perisher is slightly more complicated. The true inverse demand function is
P = 100 - S if S ≤ 33.33, P = 200 - 4S if S > 33.33
After knowing this, Vito and Pedro concluded that the profit maximizing level of output for this new inverse demand function must either be the one found in (a), or the one found in (b).
(c) Do you agree with them? Why or Why not? Find the profit- maximizing level of output for the true inverse demand function given above.