[40 pts total] Assume a household currently earns an income of $1200/month. The household spends their income either on housing or on "all other things". Price of housing is $2 per unit of quality. This utility maximizing household currently lives in an apartment that is of 240 quality level. Assume that housing is a normal good (demand increases with income), and the household has a conventional convex utility function. a) Show on a graph, the budget line and the optimal choice by using a conventional convex utility curve. Label your axes ($ on the vertical, quality (not rent) on the horizontal axis), and mark the optimal point carefully. Call this Uo. b) Now assume that the government offers public housing that is of 400 quality level, where tenants pay monthly rent that is equal to 40% of their income. Show on your graph the public housing consumption bundle point, and the corresponding utility level curve (call this U1). Is the household better/worse off with this option? c) How much does public housing cost to government per tenant (assume no production inefficiencies)? d) Show the effects of a housing voucher (that has the same cost to government as the public housing) on the tenant. Draw the new budget line carefully by showing where it intersects the axes. Is the consumer better/worse off compared to public housing? Use an alternative utility curve and name it Uz to illustrate your