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The integrated hazard for mortality for a group of lives over the period (0, ?), where r is measured in weeks, is being modelled by the function: H(t) =1- {1 + exp[(t -2)/3]}-1 (i) Find an expression for h(), the hazard function at time /. [2] (ii) Sketch a graph of h(t). [5] (iii) Suggest a context where a hazard function with this shape might be appropriate. [2] [Total 9](3) (50 POINTS) SHORT-ANSWER QUESTIONS. (a) (10 POINTS) If the average product of labor (AP,) is rising, then the marginal product of labor (MPL) must be rising as well. TRUE, FALSE, or UNCERTAIN? Explain your answer. You will be graded solely on your explanation. (b) (10 POINTS) Suppose diminishing returns set in from the very beginning, i.e., the marginal product of labor falls from the second worker onwards, without ever increasing. What does this imply for the shape of the marginal cost (MC) curve? Explain your answer. (c) (10 POINTS) The marginal product of the last unit of capital (MPk) hired by a farmer is 200 bushels of corn, whereas the marginal product of the last unit of labor (MP,) is 120 bushels of corn. The wage rate (w) is $12 an hour, and the rental rate on capital (r) is $20 an hour. The producer should use more capital and less labor. TRUE, FALSE, or UNCERTAIN? Explain your answer. You will be graded solely on your explanation. (d) (10 POINTS) The short-run average total cost can never be less than the long run average total cost. TRUE, FALSE, or UNCERTAIN? Explain your answer. You will be graded solely on your explanation. (e) (10 POINTS) In the short run, should a competitive firm ever produce when it is making a loss (a negative economic profit)? Why or why not? In the long run, should a competitive firm ever produce when it is making a loss (a negative economic profit)? Why or why not?(1) (30 POINTS] Use FIGURE 1 (on Page 4) to answer this question. It shows the isoquants Q = 50 and Q = 200 where Q = output, K = capital and L = Labor, and the isocost lines for the following levels of costs: $500, $1000, $1500, $2.000 and $2.500. The wage rate (w) is $100 and the rental rate of capital (r) is $50. (a) (8 POINTS) What combination of K and L should the firm use to minimize the total cost of producing 50 units of output? What combination of K and L should the firm use to minimize the total cost of producing 200 units of output? (b) (4 POINTS) In words, describe the expansion path in FIGURE 1. (c) (4 POINTS) Is there increasing, decreasing, or constant returns to scale? State the reason for your answer. (d) (6 POINTS) Complete the following table: Output Total Cost Average Cost 50 200 Note: The entries for the total cost should be the lowest total cost at which the corresponding level of output can be produced. (c) (4 POINTS) Without actually computing the Marginal Cost, will Marginal Cost be shove, below, or the same as Average Cost? State the reason for your answer. (0 (5 POINTS) If the wage rate decreases, will the isocost lines get steeper, flatter, or be unaffected? State the reason for your answer. Will the firm now (Le, after this wage decrease) use less, more or the same amount of labor? Will the firm now (Le, after this wage decrease) use less, more or the same amount of capital? State the reason for your answer. (2) (20 POINTS) Use FIGURE 2 (on Page 5) to answer this question. It shows the representative firm's short run marginal, average, and average variable cost curves in the left-hand side graph, and market demand and market supply curves in the right-hand side graphs. (a) (3 POINTS) What is the equilibrium price in the market (P]? What is the firm's marginal revenue [MR]? I am looking for numerical answers here. Explain your answer in one. sentence. (b) (2 POINTS) What are the two conditions for short-run profit maximization? A couple of sentences would suffice. (c) (3 POINTS) What is the firm's profit-maximizing output? I am looking for a numerical answer here. Explain your answer in no more than the sentenced (d) (6 POINTS) At this output level, what are the firm's (1) total revenue, [ii] total cost, and (ill) profit? I am looking for numerical answers here. Show all your work. (e) (3 POINTS] What is the firm's short run supply curve ( in the graph]? Describe it in words. (0) (3 POINTS) What will happen to the market price in the long run? Explain your answer in no. more than two sentences.Garden Sales, Inc., sells garden supplies. Management is planning its cash needs for the second quarter. The company usually has to borrow money during this quarter to support peak sales of lawn care equipment, which occur during May. The following information has been assembled to assist in preparing a cash budget for the quarter: a. Budgeted monthly absorption costing income statements for April-July are: April May June July Sales $ 550,000 $ 750,000 $ 450.000 $ 350,000 Cost of goods sold 385.000 525.000 315.000 245,000 Gross margin 165,000 225,00D 135 000 105,000 Selling and administrative expenses: Selling expense 75,000 95,000 56,000 35,000 Administrative expense" 42.500 56,800 35.000 33,000 Total selling and administrative expenses 117,500 151,800 91,000 68,000 Net operating income $ 47.500 $ 73.200 $ 44.000 $ 37.000 "Includes $17,000 of depreciation each month. b. Sales are 20% for cash and 80% on account. G. Sales on account are collected over a three-month period with 10% collected in the month of sale; 80% collected in the first month following the month of sale; and the remaining 10% collected in the second month following the month of sale. February's sales totaled $165,000, and March's sales totaled $225,000. d. Inventory purchases are paid for within 15 days. Therefore, 50% of a month's inventory purchases are paid for in the month of purchase. The remaining 50% is paid in the following month. Accounts payable at March 31 for inventory purchases during March total $101,500. e. Each month's ending inventory must equal 20% of the cost of the merchandise to be sold in the following month. The merchandise inventory at March 31 is $77,000. f. Dividends of $25,000 will be declared and paid in April. g. Land costing $33,000 will be purchased for cash in May. h. The cash balance at March 31 is $47,000; the company must maintain a cash balance of at least $40,000 at the end of each month. i. The company has an agreement with a local bank that allows the company to borrow in increments of $1,000 at the beginning of each month, up to a total loan balance of $200,000. The interest rate on these loans is 1% per month and for simplicity we will assume that interest is not compounded. The company would, as far as it is able, repay the loan plus accumulated interest at the end of the quarter. Required: 1. Prepare a schedule of expected cash collections for April, May, and June, and for the quarter in total. Schedule of Expected Cash Collections April May June Quarter Cash sales Sales on account February March April May June Total cash collections2. Prepare the following for merchandise inventory: a. A merchandise purchases budget for April, May, and June. Merchandise Purchases Budget April May June Budgeted cost of goods sold Total needs Required inventory purchases b. A schedule of expected cash disbursements for merchandise purchases for April, May, and June, and for the quarter in total. Schedule of Expected Cash Disbursements for Merchandise Purchases April May June Quarter Beginning accounts payable April purchases May purchases June purchases Total cash disbursements3. Prepare a cash budget for April, May, and June as well as in total for the quarter. (Cash deficiency, repayments and interest should be indicated by a minus sign.) Garden Sales, Inc. Cash Budget For the Quarter Ended June 30 April May June Quarter Beginning cash balance Add collections from customers Total cash available Less cash disbursements: Purchases for inventory Selling expenses Administrative expenses Land purchases Dividends paid Total cash disbursements Excess (deficiency) of cash available over disbursements Financing: Borrowings Repayment Interest Total financing Ending cash balance