A firm has newly developed a unique digital school bench solution for kindergartens, schools, and universities, with the following demand P and average costs AC:

P = 3000 - 3Q

AC = 1500 = constant

where P is the price per unit and Q is the number of units measured in 1000.

There are neither substitutes nor competition for this firm. The authorities put a max price of 2000 per unit to promote a wide and quick distribution of the school bench solution.

a. How do the producers' profits and market power change as a consequence of the price regulation for the school bench solution? Hint: use the Lerner index to calculate and discuss the market power

b. The authorities wish maximum production volume for the school bench solution from a. and considers adjusting the max price accordingly. Which max price gives the highest production and how much will the firm produce?