War will be costly for India, however, it will be much more costlier for China. And if India doesn't give a strong response to this current event, it will continue to be seen as a soft state and even smaller countries will keep on taking a bite of it every now and then.
I understand we Indians are very emotional and are afraid to lose people. This has a lot to do with close family upbringing and probably lots of bollywood family dramas. The scare tactics of mutilation of bodies of soldiers (by Pakistanis as well), does affect our psyche. It doesn't scare us but it makes us emotional, it rattles us. We don't want to lose men like this. This makes us more reactive in policy than proactive - except for the era of Indira Gandhi. Probably she didn't think that much of consequences, therefore she dared.
But this is not a the case with countries like China, Pakistan, America and most other countries. These countries can easily use few men as disposables for a broader national objective. Americans keep on losing men around the world all the time, but they hardly ever react emotionally such as we Indians demand after any attack on us. But then Americans keep on proactively pursue their larger objectives. They are not even afraid to lose men just to secure some cheaper oil for their country.
Anyway, back to my main point, Even though we Indians are very emotional and attached to the loved ones(including our countrymen), we are also very patriotic, much more than Chinese. Chinese national patriotism is not even close to the level of Indian patriotism. Chinese people's only affection is towards their own Chinese heritage, but not to the China mainland or Chinese communist party. Once they leave China, they are happy to speak against Chinese government and never return to China again. They will never back their government in the event of "do or die" all out war. They have lot of regional factional division as well. Hence, Chinese government can't afford a full scale war with India. They will definitely do a lot of aggressive posturing and try for a intense but short conflict but not full scale all out war. To counter this, India has to go for full scale war. Activate all of the border with China, not just Ladakh and attack eastern China especially. That's the only way to make China back off and probably to defeat them in war. Full "Do or Die" attitude.
Keep in mind, there will be damage to the economy due to war, but this damage will be much bigger for Chinese. And Chinese will never go for any war where they cannot gain substantially from it. While Americans might even see this as an opportunity to uproot communism from China, and take care of their biggest competitor as world power, once for all.
Bigger economic damage is one of the reason why India doesn't go for a war with Pakistan. They have nothing to lose compared to us. Same applies to China. They have much more to lose than us and nothing to gain. At least nothing that can help them economically. They have nothing to gain from the barren land of Ladakh and they are not definitely gonna suffer economic damage capturing Kashmir just to hand it over to Pakistan.