Hello, could you please help me to resolve this problem? Thank you.

A consumer with utility function (0, 1 ) = ln(0 ) + 1.2 ln(1) is confronted with endowments 0 = 500 and 1 = 550. Calculate the optimal consumption in both periods using the Lagrangian approach if the market rate of interest is 8%.

b) Now assume the economy consists of only two consumers; the consumer from above (consumer #1) and consumer #2 with utility function #2 (0, 1 ) = ln(0 ) + 1.05 ln(1) and respective endowment position 0 = 300 and 1 = 400.

(i) Describe the equilibrium in the capital market of this economy. What are the conditions for equilibrium?

(ii) Calculate the equilibrium market rate which clears the capital market.