01 May Examples- Changes in the supply of Avocados Draw one graph for each case Bad weather in California caused a loss of half the world’s avocado crop Avocado is cultivated in Ghana for the first time Automated avocado pickers replace harvesting the avocado crop by hand Price of land in Mexico became cheaper, and Mexico produces large quantity of avocados.
ghored. I Y, is the firm’s output in period t, the cash flows from the firm to the owners during the two periods will then be: II -Y,-I 1I-Y+(1-5)K2 Equation (4) includes the revenue from the sale of the firm’s remaining capital stodk at the end of period 2. Output in each period is given by a Cobb-Douglas production function: Y-AK,t 1,2 The term A is productivity. a) To set the problem up, sub equations (3) and (4) into (2). Then sub in the production function (equation (5) for period 2. Finally, use equation (1) to eliminate K, where it appears, which will allow you to highlight gross investment, I. Now you are ready. Start by taking the 1st derivate of the resulting 1 Labour costs would in any event drop out of the final equation.
PBBLBB tracer equation with respect to L. Next, based on the expression you found, show’that the optimal level of investment has the following form: r+δ What interpretation would you give to Y, in equation (6)? Hint: For period 2 profits, first evaluate the marginal product of capital (MPK,.) as it relates to Y2 and K2 and then use equation (1). b) Suppose now that the firm has to pay taxes on its overall profits. Note that based on Canadian tax law the firm can deduct all costs, which in this case is assumed to be depreciation. Equations (3) and (4) now become: Derive a new investment equation based on the existence of the tax on profits. Discuss how the existence of the profit tax affects investment. Would an increase in the tax rate lower investment?
c) With taxes in place, debt financing is introduced. In particular, assume that depreciation, 6K, is financed by retained earnings, while net investment, I-8K is financed entirely by debt or bonds, B. In this case, the firm’s stock of debt B, will always be equal to its capital stock, that is: B,-K, t-1,2 From the above, the firm’s revenue from new borrowing during period 1, will be equal to its net investment during that period: AB (10) Using (9) and (10) and noting that the firm’s interest payments on its debt will be rB,-rK,, the net cash flow in each period will be: 3
(12) The above assumes that the firm must pay off all of its debts with interest at the end of the period. Allowing for interest and depreciation deductibility, the tax bill faced by the firm in each period will be: (13) Based on the above, derive the firm’s investment function. Does the profit tax affect investment? Is the tax system neutral towards the choice of financing? Be sure and explain your results. d) Go back to the original model (equations (1) through (5)) and now assume that there are adjustment costs arising with the introduction of new capital. In particular assume that the relationship is linear: (14) Derive an investment equation that shows the role of installation costs. What aspect of the equation is affected by this change in the model? [Note: To simplify your work, assume that the cross product cxr 0and can safely be ignored; in point of fact, it would be small.] t14 /6
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