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Unformatted text preview: 204 CHAPTER 8. FIRMS SUPPLY CURVES Answers to Problems on Firms Supply Curves and Market Supply Curves. Answer to Problem 8.1. What is a firms shutdown point? Answer. It is a point with two coordinates. One coordinate is the shutdown price, measured in dollars per output unit, equal in value to the firms minimum average variable cost. The other coordinate is the output level at which the minimum average variable cost is achieved. This is the output level at which the firms marginal and average variable costs are equal. See Figure 8.4. Answer to Problem 8.2. Suppose a firm faces a price of p = $8 per unit for its product. The firms marginal and average variable costs are displayed in Table 8.4. The firm is stuck with 10 units of capital. The rental rate is r = $3 per capital unit. Table 8.4: Output Level Marginal Cost Average Variable Cost (output units) ($/output unit) ($/output unit) 1 12 12 2 9 10 50 3 6 9 4 5 8 5 4 7 20 6 5 6 83 7 6 6 71 8 8 6 88 9 10 7 22 10 13 7 80 11 16 8 67 12 20 9 50 13 25 10 69 14 32 12 21 (i) What is the size of the firms fixed input cost? Answer. The firm has 10 units of fixed capital, each costing $3, so the firms fixed input cost is $30. (ii) What is the value of the firms shutdown point? (Remember, the firms shutdown point has two coordinates its height on the price axis and how far it is along the horizontal output axis.) 205 Answer. The shutdown point is the minimum point on the average variable cost curve so all we need to do is look down the average variable cost column for the lowest average variable cost. This is $6 71 per product unit, achieved at an output level of 7 product units. Thus the firms shutdown point is ($6 71 per product unit, 7 product units). (iii) At what price levels p for its output does the firm increase its loss by producing? Answer. The firm will worsen its loss by producing if the price of its product is less than its shutdown price, which is the height of the shutdown point; i.e. for p &lt; $6 71 per product unit. (iv) Complete Table 8.5 by entering the firms profit-maximizing output level for each price level p . Table 8.5: Price, p $0 $2 $4 $6 $8 $10 $12 $14 $16 $18 $20 Output, q 7 &amp; 8 8 &amp; 9 9 10 10 &amp; 11 11 11 &amp; 12 (v) What is the firms supply curve? How is it related to Table 8.5? Answer. The firms supply curve is a graph with the firms output level plotted on the horizontal axis and the per unit price of the firms product plotted on the vertical axis. Particularly, the supply curve is a graph that starts at the origin and rises straight up the vertical axis to the height of the shutdown point ( i.e. to the height of minimum average variable cost, which is $6 71 per product unit). The graph then jumps across to the firms shutdown point ($6 71 per product unit, 7 product units) and then is the part of the firms marginal cost curve that continues upwards and to the right from the shutdown point. Table 8.5 above shows the values of this graphthe right from the shutdown point....
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- Spring '08