Consider the economy with capital and private debt but without money studied in class. Assume the endowment vectors are (y,0) for lenders and (0, y) for borrowers. Suppose the production function is f(k)=k and u(c, c) = ln c + In c. a. Find the equilibrium gross interest rate r. (Remember that r> 0. Note that you may obtain more than one value of r*. Hint: use the fact that one of the roots of the equation you will be solving is r= 1.) b. Find the value(s) of k. c. Find the values of consumption in both periods for borrowers and lenders?