$1.$ This problem considers tax arbitrage by a multinational corporation$$M Corp. M Corp. produces one good, the GyroPhone. A GyroPhone is a smart phone with a unique feature: it has a built in gyroscope which is activated whenever the user takes or initiates a call. In order to $$control$$ the phone, the user must grip the phone tightly and resist the motion of the gyroscope. Thereby, the user builds wrist strength. M Corp. is incorporated in country M$,$ a country with a moderate corporate tax rate, M $=0\mathrm{.}50.$ GyroPhones are a niche product that appeals only to consumers in country H$,$ a country with high corporate tax rate, H $=0\mathrm{.}50.$

To reduce manufacturing costs, M produces GyroPhones in country L$,$ a country that happens to have a very low corporate tax rate, L $=0\mathrm{.}05.$ M$$s wholly owned subsidiary, L$,$ located in country L$,$ buys commodity inputs in country L and uses these inputs to produce GyroPhones. The cost of the inputs required to produce one GyroPhone is given by c $=1.$ As well as input commodities, L may have to make royalty payments, R $0,$ to M for using M$$s intellectual property in the production process. All of L$$s after$-$tax profits are remitted to M through a dividend payment.

GyroPhones produced in L are sold by L to another wholly owned subsidiary of M$,$ H$,$ located in country H$.$ The transfer price, pT $,$ charged by L to H for GyroPhones is represented by pT $.$ These phones are sold to consumers in H for a price, pC $=2.$ H can sell exactly n $=1000$ phones. All after$-$tax profits earned by H are remitted to M through a dividend payment.

Assume that royalties $($passive income$)$ are taxed at residence and profits $($active income$)$ are taxed at source and that the tax authorities in M$,$ L$,$ and H will allow M to freely choose transfer prices and royalty payments.

a$.$ What combination of transfer price, pT and royalty payments, R$,$ maximizes the after$-$tax profits of M$?$ Because tax payments in countries H and L are never negative, you can assume that pT $$ pC and pT $$ c$.$

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b$.$ In practice, what sort of tax regulations might be imposed in countries H and M to limit M$$s ability to set transfer prices?

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c$.$ What practical problems might countries H and M have when trying to restrict company M$$s choice of transfer prices and royalty payment?