Question

In a two period model, a consumer is maximizing the present discounted utility
𝑊𝑡 = ln(𝑐𝑡) +$\frac{ 1}{ 1 + }$ ln(𝑐𝑡+1)
with respect to 𝑐𝑡 and 𝑐𝑡+1 and subject to the following budget constraint
$𝑐_𝑡 +\frac{ 𝑐_𝑡+1}{ 1 + 𝑟} ≤ 𝑦_𝑡 +\frac{ 𝑦_𝑡+1 }{1 + 𝑟 }$
where 𝑐𝑖 and 𝑦𝑖 are the consumption and income in period 𝑖 (𝑖 = 𝑡,𝑡 + 1) respectively, 𝜃 ∈ [0, ∞) is the time discount rate and 𝑟 ∈ [0, ∞) is the rate of interest. Suppose, consumer is in the interior equilibrium and 𝜃 = 0.05 and 𝑟 = 0.08. In equilibrium, the ratio $\frac{𝑐_𝑡+1}{ 𝑐_𝑡}$ is equal to _____ (round off to 2 decimal places).

Answer 1

The correct answer is: 1.02 or 1.04(approx.)