What's Joe's Optimal Combination of Consumption Today and Consumption Tomorrow - Economics Assignment Help

Assignment Task:

Task:

• Joe's utility function is given by lJ = 1n(c,) + 131n (c2) where c, is Joe's income in this year and c is Joe's income next year. He has y, = 10 units of income today and v — 5 units of income tomorrow. Assume the price of consumption today is 1 (one). 
• If the interest rate is 10%, what is Joe's budget constraint? 
• (5 marks) 
• . If the interest rate is r, what's Joe's optimal combination of consumption today and consumption tomorrow? (5 marks) 
• . If Joe had nowhere to borrow, what would be his autarky interest rate? What happens to it if b) decreases? (5 marks) 
• . Let Joe be in an autarky equilibrium. Joe meets Jim, who has preferences identical to Joe's and endowment of 5 units of income today and 10 units of income tomorrow. What would be the equilibrium interest rate on the competitive market of these two consumers? 

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