He taputapu te pūnga hiko e penapena ana i te utu hiko me te pūngao pūmanawa . Ko te pūnga hiko māmā he mea hanga mai i ngā pereti kawe hiko e rua, i ngā rau rānei e whakanohoia tata ana tetahi ki tetahi engari kāore e pā, e wehea ana e te ārai hiko, e te korehau rānei. Ko te kawe hiko he rauemi e taea ai te kawe i te iahiko hiko, pērā i te konganuku, ko te ārai hiko he rauemi kāore e taea te kawe i te iahiko hiko, pērā i te kirihou.
I te tīmatanga, he kore hiko ngā kaiārahi e rua. Kia pai ai te utu o tētahi kaiārahi, kia kino hoki te utu o tētahi, me whakawhiti ngā irahiko mai i tētahi kaiārahi ki tētahi. Kei runga i te mata o ngā ngota ngā irahiko, nō reira he ngāwari te kawe. I muri i te nekenga o ngā irahiko mai i tētahi kaiārahi ki tētahi atu, he nui rawa ngā irahiko o tētahi kaiārahi (he korenga o ngā porotana) ā, ka kino te utu, ko te kaiārahi kē atu he nui rawa ngā irahiko (he nui rawa ngā porotana) ā, ka pai te utu. Kei te kaupapa o te penapena pūngao hiko i roto i ngā kaiārahi tētahi whakamārama taipitopito mō te tukanga utu i tētahi pūnga.
E ai ki te whakaahua taha, ko tētahi o ngā pereti arataki he utu pai (+Q) ko tētahi atu pereti arataki he utu kino (-Q). He rite tonu te nui o te utu hiko i runga i ia pereti engari he rerekē te tohu, nō reira ko te utu katoa he kore (QQ=0). Ko te noho mai o ngā utu hiko o te rahi kotahi me te rerekē te tohu i runga i ia pereti ka puta he rerekētanga pūmanawa i waenga i ngā pereti e rua. He nui ake te pūmanawa hiko o te arataki utu pai, ko te pūmanawa hiko o te arataki utu kino he iti ake. Arā, he āpure hiko kei waenganui i ngā arataki utu e rua, ko te ahunga o te āpure hiko mai i te utu pai ki te utu kino. E ai ki te kaupapa o te pūngao pūmanawa hiko, mēnā he āpure hiko, he rerekētanga pūmanawa hiko rānei kei waenganui i ngā pereti arataki e rua, me whai pūngao pūmanawa hiko i runga i ngā pereti e rua.
Ko te pūngao pūmanawa te kaha ki te mahi i te mahi. Mena ka rongoa e te pūngao te pūngao hiko, ka taea e ia te mahi. Inaa, he maha ngā whakamahinga o ngā pūngao i roto i te oranga o ia rā. He wāhanga nui ngā pūngao i roto i ngā ara iahiko hiko, koinei te pūtake o ngā momo taputapu hiko.
