1. Heating your House
My English family is surprised that homes in LA are colder than English homes in the winter. To
understand this puzzle, we assume that agents choose whether to heat their homes with central
heating or with local heaters. Central heating costs $y = 28$ to install and the cost of raising the
temperature equals $c = 4$ per degree. Local heaters are free to install and the cost of raising the
temperature equals $c' = 8$ per degree.
Agents' preferences over indoor temperature $t$ and money spent on heating $x$ are given by
$U(t, x) = -(t - 70)^2 - x$.
Assume the outside temperature $T << 70$ (i.e. it's sufficiently low that agents will use their heating).
(a) Suppose an agent uses a central heater. What indoor temperature $t$ do they choose if they use
a central heater? What is their utility?
(b) Suppose an agent uses a local heater. What indoor temperature $t$ do they choose if they use
local heaters? What is their utility?
(c) Assume that the outside temperature $T$ equals 62 in LA and 50 in England. Which heating
system and indoor temperature do people in these two locations choose?
