18. (a) Suppose in the graph provided below is the endowment point, which represents an individual receives incomes 0 in the current period and 1 in the next period (assume this individual lives for two periods) where 0 is current consumption and 1 is future consumption. Assume this individual chooses the optimal consumption bundle on 0 for utility maximization, how much does this individual save or borrow in the current period? Suppose interest rate increases such that this individual can reach another indifference curve. Add whatever necessary to the graph in order to help you explain how to determine the substitution effect, income effect, and total effect on 0 and 1 . Can you determine if 0 and 1 are normal, income-neutral, or inferior goods? Explain why this individual is better off, unaffected, or worse off because of the interest rate increase. Is this individual likely belong to the younger or older age group? (b) Suppose the quantity of output depends on the production function (1, 2) and the use of two inputs, 1 and 2, which implies = (1, 2). In the short run, the amount of input 2 is fixed at 2 such that = (1, 2) = (1), which means the total product depends on the variable input 1 with a given level of the fixed input at 2 . Show the step-by-step derivation and explain the relationship between the average variable cost () and the input price, 1, and average product, (1), of the variable input. Then, show the step-by-step derivation and explain the relationship between the short-run marginal cost () and the input price, 1, and marginal product, (1), of the variable input. You must show step-by-step derivation