2. Solow Model. Consider a Solow-model country with population growth rate n and zero rate of technical change. Assume that optimal savings equals a fraction s of total output. The production function is Y. = a. K L. The real interest rate for borrowing and lending equals ~ Every year, a fraction 6 of the capital stock wears out. (a) Profit maximization. Suppose that a firm sells hockey sticks that it makes using its capital stock K, which it owns, and labor L, which it hires at wage w. Assume firm has the same production function as above. i. Write out the equation for the profits (K, L) for the firm, as a function of K and L. ii. To maximize profit, what is the equation that the firm's choice of capital must solve? What does this imply for the marginal product? (b) Golden Rule. We know from lecture that the Golden-rule capital stock , is defined by at the steady state where the gap between output and required investment is maximized. i. In what sense is it desirable for an economy to satisfy this condition? Wouldn't be better to be at the point where the gap between output and optimal investment is maximized? ii. Explain the condition on the marginal product of capital that is satisfied by ka . iii. How could we use the profit-maximization condition in part(a) to test whether k* in the Canadian economy is below the Golden Rule