Whenever a city permits a county to use the city streets and highways for the purpose of constructing and maintaining any highway or boulevard as part of a county system of roads pursuant to Section 1850, the board of supervisors may construct and maintain such bridge or bridges on such highway or boulevard within the city as it deems necessary, and may macadamize, pave, curb, or gutter, such highway or boulevard in such manner as it determines; and the cost or expense thereof shall be paid from the general fund of the county.