A firm sells an identical good in two separate markets. The inverse demand functions are p₁= 12 4q_1.

p₂ = 4 4 /3

q₂ where p₁ and p₂ are the prices, and q₁ and q₂ are the quantities. The firm's cost function is given by T C = 1 2 (q₁+ q₂) ² . Find the values of q₁ and q₂ that maximize the firm's profits when the firm has to charge the same price in the two markets. Compute the Lagrange multipliers and interpret them.