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question:The production function is still Y = AK^(0.5)L^(0.5). However, the initial capital stock is now 50,000 billion dollars, and the real price of capital has increased to 1200. If the nominal interest rate remains at 11%, the inflation rate drops to 0.5%, and the depreciation rate remains at 5%, what is the new cost of capital and how does it affect the current and future stock of capital?

answer:The new cost of capital is: C = (0.11 - 0.005 + 0.05) * 1200 = 186 The higher cost of capital reduces investment, leading to a lower current and future stock of capital. Current stock of capital: Depreciation = 0.05 * 50,000 = 2,500 Value after depreciation = 47,500 New production = 10,000 (assuming it remains the same) Current stock of capital = 57,500 Future stock of capital: Depreciation = 0.05 * 57,500 = 2,875 Value after depreciation = 54,625 New production = 12,000 (assuming it remains the same) Future stock of capital = 66,625

question:What is the term used to describe a character in literature who is defined by a single prominent trait?

answer:Such a character is referred to as a flat character.

question:Find the mode of the given data set: left{frac{18}{pi }, frac{9}{pi }, frac{18}{pi }, -frac{3}{pi }, -frac{14}{pi }, frac{9}{pi }, -frac{14}{pi }, -frac{3}{pi }, frac{18}{pi }, frac{9}{pi }, frac{9}{pi }, -frac{14}{pi }, -frac{14}{pi }, frac{18}{pi }, frac{9}{pi }, -frac{12}{pi }, -frac{3}{pi }, frac{9}{pi }, -frac{30}{pi }, -frac{14}{pi }, -frac{14}{pi }right}.

answer:The mode of the data set is the value(s) that appear most frequently. In this case, frac{9}{pi} and -frac{14}{pi} both occur five times, which is the highest frequency. Therefore, the mode of the given data set is left{frac{9}{pi }, -frac{14}{pi }right}.

question:What is the volume of 37.0 grams of methane ({eq}rm CH_4{/eq}) in liters at standard temperature and pressure (STP)?

answer:At STP, the standard temperature is 273.15 K and the standard pressure is 1 atmosphere (atm). Given that the molar mass of methane ({eq}rm CH_4{/eq}) is approximately 16 grams per mole (g/mol), we can calculate the number of moles (n) as follows: {eq}n = frac{m}{M} = frac{37.0, g}{16, g/mol} = 2.31, mol {/eq} Using the ideal gas law (PV = nRT), where R is the ideal gas constant (0.08206 L atm/mol K), we can find the volume (V): {eq}V = frac{nRT}{P} = frac{2.31 , mol times 0.08206 , L.atm/mol.K times 273.15, K}{1, atm} approx 51.74, L {/eq} Therefore, the volume of 37.0 g of methane at STP is approximately 51.74 liters.