5. Suppose a firm's production function is given by: q=10√/Ef + Em where Ef and Em are the number of female workers and male workers employed by the firm respectively. Suppose the market wage for female workers is $10, the market wage for male workers is $20, and the price of each unit of output is $100. Which of the following statements is correct? (a) Male workers and female workers are perfect complements in this firm's pro- duction function. (b) Male workers and female workers are not perfect substitutes in this firm's production function. (c) The marginal product of a male worker is higher than the marginal product of a female worker. (d) The marginal product of a male worker is 10 E₁+Em (e) The marginal product of a female worker is 5 Ef+Em (f) The profit maximizing inputs by a non-discriminating firm consist of one third female workers and two thirds male workers. (g) The profit maximizing inputs by a non-discriminating firm consist of two thirds female workers and one third male workers. (h) The profit maximizing inputs by a non-discriminating firm consist of equal numbers of male and female workers.

5. Suppose a firm's production function is given by: q=10√/Ef + Em where Ef and Em are the number of female workers and male workers employed by the firm respectively. Suppose the market wage for female workers is $10, the market wage for male workers is $20, and the price of each unit of output is $100. Which of the following statements is correct? (a) Male workers and female workers are perfect complements in this firm's pro- duction function. (b) Male workers and female workers are not perfect substitutes in this firm's production function. (c) The marginal product of a male worker is higher than the marginal product of a female worker. (d) The marginal product of a male worker is 10 E₁+Em (e) The marginal product of a female worker is 5 Ef+Em (f) The profit maximizing inputs by a non-discriminating firm consist of one third female workers and two thirds male workers. (g) The profit maximizing inputs by a non-discriminating firm consist of two thirds female workers and one third male workers. (h) The profit maximizing inputs by a non-discriminating firm consist of equal numbers of male and female workers.

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter11: The Firm: Production And Costs

Section: Chapter Questions

Problem 8P

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38. For the production function y = 3x₁ + 4x2 , which of the two inputs is more productive when x₁ is 1 and x₂ is 10 ? O. X1 O. X2 O. neither ; for this situation , they have equal marginal products O. cannot tell from the above information 39. Given the production function y = 3x₁ + 4x2 , what is the marginal rate of technical substitution of x₁ for x₂ ( MRSx1x2 ) when x₁ is 5 and x₂ is 5 ? O. -0.75 O. -x1 / 5 O. 5 O. -5
4. What must the relationship between marginal productivities and input prices if a firm is not choosing the optimal bundle of inputs but instead is hiring too much labor relative to the optimum?
A firm can manufacture a product according to the production function Q = 2(K)1/4 (L)3/4 where K represents capital equipment and L is labor. The company has already spent $10,000 on the 4 units capital. a. Please show the expression for the average product of labor, APL and the marginal product of labor, MPL. If workers at the firm are paid a competitive wage of $100 and the product is sold for $200 each, what is optimal level of labor usage and what is the maximum profit?
5. Suppose that a hot dog vendor uses a cart (K) and his time (L) to make and sell hot dogs. The vendor's production function is where Q is the number of hot dogs per day. Suppose that the rental on hot dog carts is $50 per day and that the vendor wants to Q = K0.3 10.7 produce 500 hot dogs per day. Use calculus to: a. derive the demand for labor. b. show that the demand for labor satisfies the law of demand. 2
In each of the following four cases, MRPL and MRPC refer to the marginal revenue products of labor and capital, respectively, and PL and PC refer to their prices. Indicate in each case whether the conditions are consistent with maximum profifits for the firm. If not, state which resource(s) should be used in larger amounts and which resource(s) should be used in smaller amounts.a. MRPL = $8; PL = $4; MRPC = $8; PC = $4b. MRPL = $10; PL = $12; MRPC = $14; PC = $9c. MRPL = $6; PL = $6; MRPC = $12; PC = $12d. MRPL = $22; PL = $26; MRPC = $16; PC = $19
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9. Consider an isoquant/isocost diagram, with labour measured on the horizontal axis and capital measured on the vertical axis, which can then be used to derive a demand for labour diagram. Following a rise in the wage rate, which of the following statements would accurately describe the changes on the firm's demand curve for labour? (a) There would be a movement up the demand curve for labour and the smaller is the substitutability between the inputs, the more inelastic will be the demand curve for labour. (b) There would be a movement down the demand curve for labour and the smaller is the substitutability between the inputs, the more inelastic will be the demand curve for labour.
Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the long run total cost function, C(q)? Sketch it on the diagram.
marke Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels. Q= 2 K L Q = 5 K L 7. Q= 1 Q = 4 Tech. K L K L K L 4 1 6. 9. 12 11 8. B 1 2 4 5. 12 15 Assuming that the price of labor (P) is $2 and the price of capital (PK) is $1, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level. To do this, complete the table below by calculating the total cost of production, filling in the missing values using the optimal (least-cost) technology at each level. (Enter your responses as whole numbers.) Q = 1 Q = 2 Q= 3 Q = 4 Q=5 Total Cost Enter your answer in the edit fielus and then click Check Answer. Help Me Solve This eText Pages Get More Help- Clear All Check Answer Cop %24 %24 48 25 %24
The following table shows different combinations of labor and capital that can produce 400 units of output. The 3rd and 4th columns give the marginal products of labor and capital at each input combination. Suppose the wage rate is w=$1 and the price of capital is r = $5, what is the optimal input combination that produces 400 units at lowest cost? Marginal Marginal Product of Product of Labor Capital Labor Capital 10 2 80 400 2 10 400 80 4 5 200 160 5 4 160 200 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a L=10, K=2 b L=2, K=10 C L=4, K=5 d L=5, K=4
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Consider the Labor Economics Question. This will provide insight into the idea of the optimal number of workers and the value of the marginal product of labor. If wages in the restaurant is $16.80 per hour and the price of a Hamburger is $8.30 and the production function for the workers is: Q = 11L – 0.25L2 How many workers should Your Restaurant employ during the lunch hour to maximize profits? 1 Point (note—the value of the marginal product of labor and the marginal revenue product are the same) We maximize profits which are total revenues less total costs: