B. If the company produced 100,000 units of goods, what is its average variable cost?

With 100,000 units, q = 100. Variable cost is 55q = (55)(100) = 5500 (or $5,500,000). Average variable cost is or $55,000.

C. What is its marginal cost per unit produced?

With constant average variable cost, marginal cost is equal to average variable cost, $55 (or $55,000).

D. What is its average fixed cost?

At q = 100, average fixed cost is or ($2,000).

E. Suppose the company borrows money and expands its factory. Its fixed cost rises by $50,000, but its variable cost falls to $45,000 per 1,000 units. The cost of interest (i) also enters into the equation. Each one-point increase in the interest rate raises costs by $3,000. Write the new cost equation.

Fixed cost changes from 200 to 250, measured in thousands. Variable cost decreases from 55 to 45, also measured in thousands. Fixed cost also includes interest charges: 3i. The cost equation is

C = 250 + 45q + 3i.

10. A chair manufacturer hires its assembly-line labor for $30 an hour and calculates that the rental cost of its machinery is $15 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 3 hours of labor for each hour of machine time, is it minimizing its costs of production? If so, why? If not, how can it improve the situation? Graphically illustrate the isoquant and the two isocost lines, for the current combination of labor and capital and the optimal combination of labor and capital.

If the firm can produce one chair with either four hours of labor or four hours of capital, machinery, or any combination, then the isoquant is a straight line with a slope of -1 and intercept at K = 4 and L = 4, as depicted in figure 7.10.

The isocost line, TC = 30L + 15K has a slope of when plotted with capital on the vertical axis and has intercepts at and . The cost minimizing point is a corner solution, where L = 0 and K = 4. At that point, total cost is $60. Two isocost lines are illustrated on the graph. The first one is further from the origin and represents the higher cost ($105) of using 3 labor and 1 capital. The firm will find it optimal to move to the second isocost line which is closer to the origin, and which represents a lower cost ($60). In general, the firm wants to be on the lowest isocost line possible, which is the lowest isocost line that still intersects the given isoquant.

15.Figure 7.10

11. Suppose that a firm’s production function is . The cost of a unit of labor is $20 and the cost of a unit of capital is $80.

A. The firm is currently producing 100 units of output, and has determined that the cost-minimizing optimal quantities of labor and capital are 20 and 5 respectively. Graphically illustrate this situation on a graph using isoquants and isocost lines.

The isoquant is convex. The optimal quantities of labor and capital are given by the point where the isocost line is tangent to the isoquant. The isocost line has a slope of 1/4, given labor is on the horizontal axis. The total cost is TC=$20*20+$80*5=$800, so the isocost line has the equation $800=20L+80K. On the graph, the optimal point is point A.

B. The firm now wants to increase output to 140 units. If capital is fixed in the short run, how much labor will the firm requireneed? Illustrate this point on your graph and find the new cost.

The new level of labor is 39.2. To find this, use the production function and substitute 140 in for output and 5 in for capital. The new cost is TC=$20*39.2+$80*5=$1184. The new isoquant for an output of 140 is above and to the right of the old isoquant for an output of 100. Since capital is fixed in the short run, the firm will move out horizontally to the new isoquant and new level of labor. This is point B on the graph below. This is not likely to be the cost minimizing point. Given the firm wants to produce more output, they are likely to want to hire more capital in the long run. Notice also that there are points on the new isoquant that are below the new isocost line. These points all involve hiring more capital.

Date: 2015-12-24; view: 1404