Question 3 The Consider the problem of a firm who produces output in the present and the future period. This firm is endowed with K units of capital in the current period which is exogenously given Ko through investment I. In particular, we have the firm can, however, choose future capital stock following capital accumulation equation: Kº= I. Note that this capital accumulation equation implies that capital is fully depreciated in each period (d=1). The firm's profit is = Y- WN - I in the current period, where Y = ZF (K,N) is output, w is wage, and N is employed labor. Similarly, the profit in the future period is given by π°= Y₁- w°N° where Yo= z°F (KN) is future output, wo is future wage, N° is future labor demand. Note that there is no value of capital left over after production in the future period due to full depreciation (d= 1). The firm maximizes the present value of profits given by Answer the following questions. 1. 2. 3. πο V = x+ 1+1 Write down the firm's profit maximization problem. Derive labor demands for both the current period and the future period as functions of K and K 2 Derive the optimal rule of investment.

f Question 2: Show the effect of the following transactions of May 2021 on the accounting equation: 2 6 11 The owner, Ms. Rose Petals, contributed R80 000 as capital contribution. Issued receipt no. 57. According to the cash register roll, the business received R5 300 for services rendered. Cashed a cheque (Cheque 03) to pay the wages of her 2 workers. They each earn R1000 per week. 30 Paid Mogale City for the water and electricity, R2 000 per cheque. Day Assets Owner's Equity + Liabilities Effect Reason Effect Reason Effect Reason (14)

be Question 2: Should a firm invest? (show all your work. Points will be deducted for no work) (20 points) A firm learns a firm has an investment opportunity that will earn future revenue 4 years from now by $160,000. The marginal cost of the physical capital today is $125,000. The firm makes this investment at an interest rate of 5%. Using this information answer the questions below 1. Should this frim make this investment? 2. What is the discounted percentage for this investment? 3. Other things being equal, could this investment be made a higher interest rate? Lower? Why, Show with numbers 4. Other things being equal, could this investment be made for longer term? Shorter term? Why?, Show with numbers

Note: Hand written solution is not allowed.

3. Consider a dynamic (two-period) representative firm's problem. This representative firm is given K unit of capital to produce in the current period. Firm can choose (current-period and future-period) labor demands and investment (to adjust future- period's capital stock) to maximize its present-value lifetime profit. Given that the market interest rate is r and the capital depreciation rate is & after production in each period. Let's further assume that this firm sells all the capital after future-period production. (a) Clearly definite the profit functions for both periods and write down this repre- sentative firm's problem. (b) Write down the optimal condition on investment. Intuitively explain the optimal condition. (c) Suppose K increases, graph the change of investment curve. Intuitively explain the changes on the graph you just drew.

(b) Assume the economy is at steady - steady until the rate of depreciation suddenly experiences a permanent increase at 1. Use the following parameter values: A = 1, x = 0.5L 1,s = 0.2 where s is the saving rate and > is the depreciation rate, and complete the following table (show your working for row 2 only): Round to two decimal places. You may, though are not required to, use Excel or similar for this task. Also pls help me Comment on how persuasive the results of part (b) are. (b) Assume the economy is at steady-steady until the rate of depreciation suddenly experiences a permanent increase at t = 1. Use the following parameter values: A = 1 L= 1 a = 0.5 8 = 0.2 8 = (0.10 t<1 (0.15 t≥1 where s is the saving rate and 8 is the depreciation rate, and complete the following table (show your working for row 2 only): Period (t) Capital Stock (K) Output (Y) Saving (St) Investment (I) 1 Consumption (C₁) (This row will be your steady state values from part a). 2 3 4 9 10 Round to two…