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Chapter 7 Key

# Chapter 7 Key - Chapter 7 Homework Key Please Answer All...

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Chapter 7 Homework Key Please Answer All Questions on this homework set. 1. Coldwell Banker is employing 10 acres of land and 50 tons of cement to produce 1,000 parking spaces. Land costs \$4,000 per acre and cement costs \$12 per ton. For the input quantities used, MP L = 50 and MP C = 4. a. Draw Coldwell Banker’s isocost line. Make sure you label all appropriate points. land cement 4060 812 a 50 10 Q=1,000 b. Is Coldwell banker minimizing their cost of producing parking 1,000 spaces with their current input usage? Show graphically the situation. No. To be the cost minimizing level, the slope of the isoquant must equal the slope of the isocost line. The slope of the isoquant is the ratio of the marginal product of land to the marginal product of cement, which is 50/4=12.5. The slope of the isocost is the ratio of the price of land to the price of cement, which is 4,000/50=80. The slope of the isoquant is less than the slope of the isocost line. Therefore, they are using too much land and not enough cement given the information above. This is point a in the above graph. They should build up rather than out.

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2. Suppose a firm is in equilibrium using 10 units of capital and 8 units of labor to produce 100 units of output. Their operating budget is \$500 and the price of capital is \$10 and the price of labor is \$50 per unit. Now suppose the price of capital falls. Using and isoquant-isocost diagram, show the effect on the firms optimal use of capital and labor. Will the firm be producing a higher, lower or the same level of output as before? l k 10 50 10 8 Q=100 Q=150 The initial equilibrium is where the isoquant, q=100, is tangent to the isocost line given by the y axis of 50 and the x axis of 10. If the price of capital falls, then the isocost line rotates outward from the x axis. With 10K and 8L, the firm is no longer maximizing output. The could use more capital and less labor, holding cost constant, and move to a point where a new isoquant is tangent to the new isoquant line. Say Q=150. Remember, the two isocost lines represent the same \$500 initial cost.
3. Suppose a firm is in equilibrium using 10 units of capital and 8 units of labor to produce 100 units of output. Their operating budget is \$500 and the price of capital is \$10 and the price of

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