Given total house value, , mortgage interest, , property tax rate, , depreciation rate, , housing capital gains, , rental per square footage, and purchase price per square footage, . The tax rate for owner occupiers is given by , and for landlords is . Assume the US tax treatment of housing costs and benefits.

a. First, express the pre-tax total cost to homeowners (owner-occupier). Then, express the per square footage user cost to homeowners. Then, derive the post-tax per square footage user cost to homeowners.

b. Repeat the same process as in (a), but for landlords.

c. Express the pre-tax and post-tax revenue for landlords.

d. Combining the post-tax terms in (b) and (c), express the landlords profit function, and derive the per square footage user cost to renters.

e. Mathematically prove this models prediction regarding who will rent and/or own. Is this prediction realistic? Why or why not? Suggest ways to improve the model.

f. Draw a diagram to identify owners and renters in the improved model.

g. With this improved model, predict what would happen to the share of owner-occupiers as a result of the following external shocks: i. Increase in mortgage rate, . ii. Increase in property taxes, . For both (i) and (ii), draw the diagram, explain changes in ownership share, and provide the intuition for that change.