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.

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.