TIC is a multinational firm that comprises a domestic manufacturing division $($D$)$ and a foreign retailing division $($F$).$ D can make widgets and gadgets in a fully automated factory. It takes $30$ minutes of machine time to make either a widget or a gadget. Machine capacity is $10,000$ hours per month. Manufacturing monthly overhead, all fixed, is $$800,000,$ and is allocated to products on the basis of machine time under D$$s full absorption costing system.

Each widget uses $$60$ of material. Each gadget uses $$70$ of material and sells for $$130.$ D currently uses all of its capacity to make $20,000$ gadgets each month.

F wants to sell $4,000$ widgets to customers in Greece. It can buy the widgets from an unrelated wholesaler for $P per unit, or buy them from D$.$ TIC wants to maximize the sum of the profits earned by D and F$.$

$($PLEASE SHOW STEPS$)$

Question $1.$

Find the external price $P per widget at which TIC would be indifferent between having the foreign subsidiary buy the widgets from an unrelated wholesaler and having D produce the widgets and sell them to F$.$

Question $2.$

Transfers within TIC use a transfer price equal to $110$ percent of full cost. What is the transfer price of a widget?

Question $3.$

Suppose the external price $P is $130$ per widget. What transfer price divides the gain or loss to TIC from internal widget production, relative to the alternative of purchasing the widgets externally for $$130$ each, equally between the two divisions?