A firm faces demand P$=100-$Q and constant marginal cost of $10.$ Due to asymmetric information, the manufacturing division of the firm determines the price charged to the sales division of the firm $($transfer price$)$ and the sales division has no information about the production cost of the manufacturing division.

Task $1$: Determine the profit maximising transfer price of the OVERALL firm, that is$,$ the price that the manufacturing division should chatge the sales division for the product, assuming they want to from maximise at the overall firm level $($not divisional level$).$ Explain in economic terms.

Task $2$: Derive the transfer price, that is$,$ the price that the manufacturing division charges the sales division, when the manufacturing division exploits the asymmetric information. This is the price that maximises profit for the manufacturing division, but not the overall firm. Show that the overall profit of the firm is lower than the result from Task $1.$

Task $3$: Compute the profit that the manufacturing division makes and the profit that the sales division makes. Explain in economic terms.