The amount people can afford to pay doesn't change, but the cost of the house does change.

Assume a 30 year mortgage. If the interest rate is 2%, and I spend 1.5k a month on my mortgage, I can afford a mortgage of 406,000 and own the home at the end. However, if interest rates are 10%, even if I'm still earning 1.5k a month, I can only afford a mortgage of 171000 in order to pay it off by the end. You can double check my figures using this calculator - https://www.bankrate.com/uk/mortgages/mortgage-repayment-cal...

Given that deposits are usually at a minimum 10% of the house price, it's very hard for first-time buyers to gather that amount of money - while people who have purchased before can sell their existing home.

The issue the paper describes is that interest rates have gone down, so house prices have gone up, _and at the same time_ it's harder to get your first mortgage (i.e. you need a larger deposit) - which most new buyers cannot afford.