Suppose a firm has a simple production function of the form x=In(1+K), where K is the...

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Suppose a firm has a simple production function of the form x=In(1+K), where K is the firm's total capital stock. The firm has an initial capital stock K, and must borrow at interest rater in order to purchase new capital stock (let the unit price of capital good be equal to 1). Noting that the firm's total capital stock equals its initial stock augmented by its desired investment level (K=K, +1), assume that the firm's expected profit from current investment is determined by the output price it expects to receive in the future, denoted p. Given this information, express the firm's profit as a function of p, r, and I, then derive and illustrate the firm's profit-maximizing level of investment as a function of the current interest rate and the firm's expected future price. What is the effect of changes of each of these parameters on the firm's level of desired investment? Illustrate and explain. Suppose a firm has a simple production function of the form x=In(1+K), where K is the firm's total capital stock. The firm has an initial capital stock K, and must borrow at interest rater in order to purchase new capital stock (let the unit price of capital good be equal to 1). Noting that the firm's total capital stock equals its initial stock augmented by its desired investment level (K=K, +1), assume that the firm's expected profit from current investment is determined by the output price it expects to receive in the future, denoted p. Given this information, express the firm's profit as a function of p, r, and I, then derive and illustrate the firm's profit-maximizing level of investment as a function of the current interest rate and the firm's expected future price. What is the effect of changes of each of these parameters on the firm's level of desired investment? Illustrate and explain.