Rosenberg produces board games using Labour(L) and machines(K) as inputs. His board game production function is given as follows:
Q = f(K; L) = 2L^2K2 Rosenberg faces labour costs of $3 per unit of labour and capital costs of $5 per unit of capital. Rosenberg wants to produce as many board games as possible but only has $1000 at his disposal and is not able to spend more than that. Describe your answer and give examples.
Required:
(a) What is the optimal choice of L and K for Rosenberg? How many board games are produced at this amount of L and K?
(b) Due to a short supply of labour, labour costs now rise to $5 per unit of labour. What is the new optimal choice for the firm?