Assume that the parameter values in the model of housing tenure choice are given as:

mortgage interest rate depreciation rate accelerated depreciation

i = 0.03 d = 0.02 e = 0.02

property tax rate capital gains rate landlord's tax rate

h = 0.02 g = 0.04 = 0.35

Assume that we are comparing dwellings with the same value per square foot (v), so it can be dropped from the discussion. Let's denote the income tax rate by . Calculate the following:

(a) user-cost per unit for owner-occupiers as a function of . Label it u-co-o

(b) user-cost per unit for renters as a function of . Label it p.

(c) the cut-off income tax rate that separates renters and owner-occupiers (round-off your answer at two decimal points). Label it .

(d) Explain which group of tax payers chooses to be renters versus own-occupiers.

Draw a clearly labelled diagram with on the x-axis, depicting elements listed below:

(e) both user-cost lines u-co-o and p from (a) and (b) above.

(f) the calculated in part (c).

Suppose that the landlord's tax rate increases to * = 0.40. Using this new value,

(g) compute the new user-cost(s), resultant cut-off tax rate .

(h) On a clear diagram, draw and label original and new user-cost line(s), and . *

(i) How do the relative sizes of renters and owner-occupiers change? Give an intuitive explanation for your answer.

Now, is back to its original value but property tax rate increases to h** = 0.03. With this value,

(j) compute the new user-cost(s) and the resultant cut-off tax rate

(k) On a clear diagram, draw and label original and new user-cost line(s), and

(Hint: this diagram is not as simple; pay attention to the slope of u-co-o.)

(l) How do the relative sizes of renters and owner-occupiers change? Give an intuitive

explanation for your answer.