Consider three households earning an after-tax income of $5,000 per month.

Each family has preferences that take the following form:

Family a: = 0.3 ln() + 0.7 ln()

Family b: = 0.5 ln() + 0.5 ln()

Family c: = 0.8 ln() + 0.2 ln()

where U denotes utility, I is internet connection speed measured in Mbps and G refers to any other good/service that the family buys. The price of I is $10 and the price of G is $100. Each family has to decide how to allocate their budget between goods I and G.

a) Which family cares about internet connection speed the most?

b) Assume that, initially, internet access is provided by private companies only. Families can select a package with their desired internet speed (I). In this part assume that the government does not provide any support for internet access, so individuals must purchase it in the private market and must pay the full price ($10 per unit). For each family, derive the combination (I*, G*) that maximizes utility given the budget constraint. Show your calculations: i.e. show all steps needed to derive the MRS and the optimal bundle (I*,G*).

c) Now suppose that the government determines that internet access is a necessity and that families should have an internet speed of at least 10 Mbps to be able to access public services offered online (e.g. online schooling). For this reason, the government decides to use tax revenue to provide an internet connection speed of 10 Mbps for free to all families. Households can now choose between the package offered by the government for free (10 Mbps) or the packages offered by the private sector with a price of $10 per Mbps. They cannot combine packages, they either choose the publicly provided Internet package or the privately provided internet package. Indicate which family would switch to the publicly provided package and why. Show your calculations. Use a graph to compare the optimal bundles in part (b) to the optimal bundles in part (c) the graph should have I on the horizontal axis and G on the vertical axis. Compute the total amount of money that the government spends on this program. In this case, is there any evidence of crowding out resulting from public provision of I?

d) Now consider an alternative option. Instead of providing free internet with a speed of 10 Mbps, the government could provide a matching grant equivalent to 1% of the family spending on good I. Following the notation from class, b=0.01. Note that this changes the price of I. Follow the lecture notes and re-compute the optimal bundle for each family. Graphically show how this policy would affect families choices. Compute the total amount of money that the government spends on this grant. If the goal is to promote internet access at the lowest possible cost for the government, is the matching grant better than public provision in part (c)? Briefly explain why.

e) Alternatively, the government could provide an unconditional cash transfer of $24 to each family. Note this is an increase in income by $24. Re-compute the optimal bundle for each family. Graphically show how this policy would affect families choices. Compute the total amount of money that the government spends on this grant. If the goal is to promote internet access at the lowest possible cost for the government, is the unconditional cash transfer better than the matching grant in part (d)? Briefly explain why.