# Question on monopolist (involves simple calculus)

QUESTION: Consider the problem of a monopolist that sells its product in two different markets $m$, with $m=1,2$. Each market has an aggregate demand function given by $1200−α_m\cdot p_m$, where $p_m$ denotes the price in market $m$, and $α_m=m$ measures the responsivity of demand to prices in market $m$. The monopolist's cost function is given by $c(q)=12q^2$, where $q$ denotes the total amount produced for all markets.

The monopolist is owned by a foreign company, so none of the monopolist's profits are received by the consumers in these markets. The law allows the monopolist to charge different pricees in different markets, but does not allow any other forms of price discrimination.

1. What is the equilibrium level of production in market $2$?
2. What is total consumer surplus in the economy (i.e., taking both markets into account)?