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Martial Arts Exchanges


Chuck and Bruce trade kicks ($K$) and punches ($P$). Chuck has 3 kicks and 6 punches to trade, while Bruce has 10 kicks and 8 punches to trade. Both Chuck and Bruce, being straight-forward martial artists, have very straight indifference curves: Chuck’s utility function is $U_C = K + 2P$ and Bruce’s utility function is $U_B = 2K + P$.

If kicks and punches cost the same amount, who trades kicks for punches?

What is the final allocation of goods after they trade?