To finish the argument, it is only necessary to note that C, the marginal cost in heat flow of internal temperature, depends on characteristics of the house such as insulation and size. If, as argued above, identical houses will tend to have the same interior temperature in both cities, then for houses that differ in C, the optimal T i will be higher the lower C is. Houses in Chicago will tend to be better insulated than houses in Los Angeles, and better insulated houses will be kept at a higher internal temperature. Hence warm houses are found in cold climates and vice versa. Internal temperature is constant over time, for reasons explained above.
T o is the average external temperature.
I assume that external temperature is always lower than internal temperature. Q.E.D. Looking back at Equation 3, we see that the budget lines must have the shape shown in Figure 1. In other words, the larger the desired temperature differential between inside and outside, the larger the optimal amount of insulation, and the smaller the cost of an additional degree of internal temperature. T o2 which is tangent to I1 at a temperature above T i1 . Since it cannot intersect I1, it must intersect B1', as shown.