The theory of consumer choice
Increasing rents are a concern for many governments and have motivated a number of policies designed to help meet the housing needs of poorer households. For this question you will be asked to analyse the impact of three different policies: the provision of public housing; housing subsidies and a cash transfer.
Suppose a family earns £1,500 per month and can either pay £0.50 per square foot in monthly rent for an apartment in the private rental, market or accept a 1,500 square foot house provided by the government at a fixed price of £500 per month.
a) In a graph with square feet of housing on the horizontal axis and ‘all other consumption’ on the vertical axis, illustrate all of the bundles in this family’s choice set.
b) Redraw the diagram in (a) and, using indifference curves, illustrate two cases where the family would accept/prefer the public housing: one in which this leads them to consume less housing than they otherwise would and another where this leads them to consume more housing than they otherwise would. Would the public housing make the family better off?
c) How much does it cost the government to provide a public housing unit to this family? (hint: what is the government’s opportunity cost of owning a public housing unit of 1,500 square feet?)
d) Now consider a rental subsidy under which the government pays some fraction of a household’s rental bill in the private housing market, effectively lowering the price per unit of rental housing. Using indifference curves and distinguishing between income and substitution effects illustrate the effects of the subsidy on the consumption of housing. Under what circumstances would this lead to a decrease in housing consumption?
e) Suppose instead that the government simply gave cash to the household. If it gave sufficient cash to make the household as well off as it is under the public housing program, would it cost the government more or less than £250? Can you tell whether under such a cash subsidy the household consumes more or less housing than under public housing?
The theory of production and costs
Many countries have minimum wage laws, which require firms to pay a minimum wage level to all employees. In this question you will be asked to consider the impact of a minimum wage on a firm’s costs and output decision.
Suppose a firm employs labor ℓ and capital k to produce output x using a homothetic, decreasing returns to scale technology.
a) At the current market wage x, rental rate of capital r and output price p, the firm has identified A = (xA, ℓA, kA) as its profit-maximizing production plan. In a diagram, with labor on the horizontal axis and capital on the vertical axis, use an isoquant and isocost curve to illustrate this production plan and explain why it must satisfy the conditions for cost-minimisation. Illustrate in your graph the set of all cost-minimising input bundles.
b) Now plot the corresponding total and marginal cost curves, assuming the wage w and rental r are fixed.
c) Suppose the government introduces a minimum wage law, which raises the cost of labor to w+m per unit. Explain and illustrate what impact this will have on the firm’s cost-minimising input choice for producing output level xA. Illustrate the impact on the firm’s total and marginal cost curves (you can use the same diagram as in b) as long as you clearly identify the new cost curves).
d) Suppose the minimum wage has made workers more productive. Illustrate and explain what impact this would have on the firm’s isoquants and cost minimising input choice.
e) Starting from the scenario described in c), now suppose that alongside the minimum wage, the government also introduces a fixed tax that raises the cost of capital by the same proportion m – so the new cost of capital is r+m. Explain and illustrate what impact this will have on the firm’s cost-minimising input choice for producing output level xA and illustrate the impact on the firm’s total and marginal cost curves.