Optimal consumption. Solve the following optimal control consumption model: max fctg Jct Z 5 0 bt

Optimal consumption. Solve the following optimal control consumption model: max fcðtÞg JðcðtÞÞ ¼ Z 5 0 bt lnðcðtÞÞdt s:t: K_ðtÞ¼  cðtÞ Kð0Þ ¼ 5; Kð5Þ ¼ 0 and where b ¼ 1 1þ0:05 is the discount factor and K(t) is the capital available to the consumer. We assume there is no capital appreciation and that only the consumption affects the Capital Path.