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- 4. For each of the following production functions, write the equation and graph the supply curve of the firm if w=20 and r=50 When the price of output is $20, how much will the firm offer to the market and what are the profits of the firm? a. Q = 10 K^.2L^.5B^.1 in the long-run with capital flexible. B is the amount of Building Space employed, which is held fixed at 1 unit in both the long-run and the short-run and has a price of $100 per unit. b. Q= (4K^.6 + 8L^.6)^ 1.25A firm's resource input, total output of labor, and product price schedules are given in the table. If labor is the only variable input, how much labor should the firm employ if the wage rate is $15 per day? Units of Labor Total Output/Day 20 30 2 3 4 5 6 7 * 3 units *4 units *5 units *6 units 38 46 54 62 Price of Good ($) $10 9 8 7 6 51. Suppose that a producer has the following production function: Q = K³L'® Where Q is output, and L and K are man-hours and machine-hour the two inputs used in the production process. 1A) Set up the cost minimization problem as shown in class - In the cost minimization problem, the cost is minimized subject to constraint production function. It is indicated as follows: Minimize wL + rK subject to constraint Q = K3 L16 A = wL + rK + (Q-K-L6) The Lagrange f unction is differentiated by K andL to calculate the minimize the cost, and W= wage rate L=Labor R= real interest rate K = capital Q = output A= parameter coefficient 1B) Determine the cost-minimize ratio of inputs where capital costs $1 per machine-hour and labor costs $4 per lab- hour. - MRTS = Marginal product of labor Marginal product of capital Q = KL!6
- Suppose you are considering hiring another worker. Also assume that you are at a firm that is operating at a point where the marginal product of labor is 5 and the price of each unit of labor is $2, and the marginal product of capital is 20 and the price of each unit of capital is $10. Should you hire another worker? If you hire another worker, what will happen to the marginal product of labor and why?13. Identify which way the labor supply curve would shift under the following scenarios. A country experiences a huge influx of immigrants who are skilled in the textile industry. Wages increase in an industry that requires similar job skills. New machines require additional maintenance over time, so that the marginal productivity of labor rises.Demand for Resources A small manufacturing company has the following daily relationship between labor and output: Units of Total Labor Product 1 2 21 3 35 52 61 65 61 7 If the firm sells into a perfectly competitive market and the equilibrium price is $3.25 per unit, compute the following: Marginal Units of Marginal Product Revenue Labor Product 1 2 3 5 7 How many workers will the firm hire is the market wage rate (includining benefits) is $30.00? Wł 3 How many workers will the firm hire is the market wage rate(includining benefits) is $20.00? 4 If the equilibrium price per unit of output dencreases, what would you expect to happen to the number of workers hired? If the firm sells in a imperfectly competitive market such that price per unit starts at $4.50 per ur declines by $0.10 per unit as more as sold, what do you think would happen to the number of labor units hired at $30.00 per unit? 5 2.
- Suppose that the demand for loanable funds for car loans in the Milwaukee area is $12 million per month at an interest rate of 10 percent per year, $13 million at an interest rate of 9 percent per year, $14 million at an interest rate of 8 percent per year, and so on. If the supply of loanable funds is fixed at $16 million, what will be the equilibrium interest rate? Instructions: Enter your answer as a whole number. * percent per yearThe idea of "economic rent" can be applied to resources other than land. What is economic rent? O The additional "pay" the owner of a resource can earn greater than its "supply price." It's when supply is greater than demand. |0|0|0 O It applies to apartment rent in large cities where rents are outrageous. OIt refers to ridiculously high taxes on entrepreneurs.Question 54 Answer the next question(s) on the basis of the following marginal product data for resources a and b. The output of these independent resources sells in a purely competitive market at $1 per unit. Inputs Inputs of a MPa of b 1 25 1 2 20 2 36 TITI 3 15 3 4 10 4 2 6 1 7 Reference REF27111 40 32 24 20 16 Refer to the above data. Assuming the prices of resources a and bare $5 and $8 respectively, what is the least costly combination of resources for the firm to employ in producing 192 units of output? a) 2 of a and 6 of b b) 4 of a and 3 of b c) 6 of a and 2 of b d) 3 of a and 4 of b
- An economy can produce leather using labor and capital and wheat using labor and land. The total supply of labor is 50 units. Given the supply of capital, the outputs of the two goods depend on labor input as follows: Labor Input to Leatheroutput of LeatherLabor Input of WheatOutput of Wheat 27 5 19.8 10 38.5 10 31.2 15 47.3 15 42.3 20 56 20 52.1 25 65.7 25 60.6 30 74.5 30 69 35 82.4 35 77.4 40 88.2 40 85.4 45 94.1 45 93.9 50 100 50 100 a. Graph the production functions for leather and wheat. b. Graph the production possibility frontier. What will happen if more labor is employed?You own a coffee shop and use both labor and capital to make lattes. Currently, the marginal product of labor is 50 lattes a day while the marginal product of capital is 20 lattes a day. You pay your labor $100/day, and you rent your Nuova Simonelli Appia Life Black 2 espresso machine for $25 a day. The price of a latte is $5. Are you employing your inputs effectively? If not, what would you do to increase efficiency?Suppose that you own a 20-acre plot of land that you would like to rent out to wheat farmers. For them, bringing in a harvest involves $30 per acre for seed, $80 per acre for fertilizer, and $70 per acre for equipment rentals and labor. With these inputs, the land will yield 40 bushels of wheat per acre. Instructions: Enter your answers as a whole number. a. If the price at which wheat can be sold is $6 per bushel and if farmers want to earn a normal profit of $10 per acre, what is the most that any farmer would pay to rent your 20 acres? $ b. What price would the farmer pay to rent your 20 acres if the price of wheat rises to $7 per bushel?
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