5. Consider a firm that uses both labor and capital in production. The price of capital is $20 per unit and the wage rate is $10 per hour. a. Draw the firm's isocost line assuming a total production cost of $100. How steep is this line (that is, what is its slope)? Be sure to clearly label the axes. b. Suppose the wage increases to $15 per unit. In which direction does the substitution effect change the firm's demand for labor and capital? In which direction does the scale effect change the firm's demand for labor and capital? c. If the firm chooses its labor and capital combination to minimize its production costs, will the marginal product of labor be higher than, lower than, or equal to the marginal product of capital? Why? (Assume that the price of labor and capital are those given in part b.)

5. Consider a firm that uses both labor and capital in production. The price of capital is $20 per unit and the wage rate is $10 per hour. a. Draw the firm's isocost line assuming a total production cost of $100. How steep is this line (that is, what is its slope)? Be sure to clearly label the axes. b. Suppose the wage increases to $15 per unit. In which direction does the substitution effect change the firm's demand for labor and capital? In which direction does the scale effect change the firm's demand for labor and capital? c. If the firm chooses its labor and capital combination to minimize its production costs, will the marginal product of labor be higher than, lower than, or equal to the marginal product of capital? Why? (Assume that the price of labor and capital are those given in part b.)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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5. A firm produces widgets using the following production function: q = K VL. The wage and the rental cost of capital are both $20. a. What is the firm's marginal product of labor? b. Does this firm have increasing, constant, or decreasing returns to scale? Explain. c. In the short run, the firm has 10 units of capital. Write an expression for the firm's short-run total cost in terms of its output: TC(q). d. Write an expression and draw a graph of the firm's short run supply curve. Be clear about the range of prices over which the firm chooses to enter rather than shut down.
3. (14 points) Let the production function be Q(K,L)=2K L. The cost of one unit of labor is w, the cost of one unit of capital is r, and the quanitity to produce is y. (a) (4 points) Set up the firm's cost-minimization problem, and clearly write down the con- Page 6 straint the firm faces. The cost minimization problem of the firm is min(KL) WL+rK. The constraint: y=2K!L!. anscribed Text (b) (5 points) What are two conditions that the optimal bundle L and K need to satisfy? Write down their expressions. Tangency: -=-; production: y = 2(K)! (L)!. (c) (5 points) Solve for the optimal bundle of L. and K that minimizes the firm's cost at y=144 by finding L and K", assuming that w $16 and r $81. By solving the system of two conditions in Part (b), it should be not that hard to get L = 162 and K* = 32.
Please give me the solution of D
1 This question is based on the following diagram. Assume that the dashed lines are parallel and that their common slope is equal to b. (That is, b represents a constant.) Moreover, assume that I in the diagram is an inflection point on the total product curve. {Note: An answer "K to N" is different from an answer "above K".} a. TOTAL OUTPUT C. AL KL M N 0 INPUT At what level of the variable input do diminishing marginal returns begin to set in? b. At what level of the variable input does the average product equal the marginal product? For what range of values of the variable input does the average product exceed the marginal product?
2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 3 8 12 15 17 K=2 10 15 19 22 24 K=3 16 21 25 28 30 K=4 20 25 28 30 31 (1) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L?
5 Question 5 A bottling company uses two inputs to produce bottles of the soft drink Dr Pibb; bottling machines, K, and workers, L. The firm's production function exhibits diminishing MRTS. At its current level of production, the firm spends 800 per day on machinery and 200 per day paying wages to its workers. At this level of production, the marginal product of the machine is an additional 200 bottles per day and the marginal product of labor is 50 more bottles per day. Is this firm producing at minimum cost? If it is minimizing cost, explain why. If it is not minimizing cost, explain how the firm can lower its cost.
4. Profit maximization in the cost-curve diagram The following graph plots daily cost curves for a firm operating in the competitive market for demin overalls. Hint: Once you have positioned the rectangle on the graph, select a point to observe its coordinates. 50 45 45 O O 40 35 35 30 PRICE (Dollars per overalls) 20 15 10 5 + 0 0 2 ATC AVC MC 46 8 10 12 14 16 18 20 20 QUANTITY (Thousands of overallses per day) Profit or Loss ?
Uncertain which options match each blank: a. Decreases, and therefore the curve shifts down b. Is unaffected, and therefore the curve does not shift c. Increases, and therefore the curve shifts up
I understand why point A is not optimal but why is point B optimal when the isoquant curve is not tangent to the isocost line at point B?
G, 5 Subject - economics
4) Suppose that a firm's production function is Q = Lº.4K0.6. The cost of a unit of labor is $8 and the cost of a unit of capital is $12. Write firm's long run cost function. Calculate the slope of isocost line. Calculate marginal rate of technical substitution. d. Suppose firm decides to produce 50 units, what is the cost minimizing combination of these two resources (labor and capital)? a. b. C.
2.)Do fixed costs refer to the long run or short run? Why?3) Suppose that labor is the only variable input in the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labor?4) What are economies of scale? What are economies of scope? What is the difference between the two?