In a two period model, a consumer is maximizing the present discounted utility 𝑊𝑡 = ln(𝑐 𝑡 ) + $\frac{ 1}{ 1 + }$ ln(𝑐 𝑡+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).

Question

In a two period model, a consumer is maximizing the present discounted utility 𝑊𝑡 = ln(𝑐 𝑡 ) + $\frac{ 1}{ 1 + }$  ln(𝑐 𝑡+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).

cdquestions Admin · Accepted Answer

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

Households	H1	H2	H3	H4	H5	H6	H7	H8	H9	H10
MPCE(in Rs.)	2800	3000	1200	3500	1400	2500	4000	1000	900	1300

Year	Population of the Economy	GDP of the Economy (in crore)
2010	20,000	25,000
2020	25,000	40,000

Correct Answer: 1.02

Solution and Explanation

Top Questions on Consumer theory

Questions Asked in IIT JAM EN exam