President Vladimir Putin of Russia recently proposed replacing in-kind subsidies such as free public transportation and rent-free apartments for government workers with cash subsidies of between \(\$ 20\) and \(\$ 120\) per month. The proposal led to widespread complaints among Russian citizens that the cash subsidies were not large enough. One reported asked, "What is a perk worth?" [Chivers, 2004]. Use an indifference curve analysis to show how to convert an inkind subsidy into a cash subsidy that leaves people equally well off.