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2 Leo's birthday is coming up and all he has in his possession is one bottle of soda. His friends get together and decide to buy him a gift. They agree on getting him some bottles of soda (s) and some fancy colorful soda making powder/shaker contraptions (f). Leo's utility function is given by U(s, f) = s + fs - f-. The soda costs p, = 1 and the powder shaker contraptions cost py = 2. His friends decide to buy him two bottles of soda (in addition to the one he already has) and one powder shaker thing, spending a total of $4. (Throughout this question, you can assume that both soda and the fancy powder things can be consumed in any fractional amount. When drawing diagrams, put soda on the horizontal axis and the powder shaker things on the vertical axis. Also, you should only be concerned about the negatively sloped portions of the indifference curves. Do not worry about portions which are positively sloped.) (a) At Leo's initial position prior to receiving the gifts, is he optimized?301 Intermediate Microeconomics. em Set #4 Production E: a. Write an equation for the short-run production function for the firm showing output as a function of labor. b. Calculate the total output produced per hour for L-0, 1,2,3,4,and5. C. Calculate the MIL for L=1 to L=5. Is MPL Diminishing? Explain d. Calculate APL for L-1 to L-5. Answer the following questions based on the following production process schedules. Suppose a firm's short-run total product schedule is given in the table below. Production Production Production Production Process (K-1) Process (K=2) Process (K 3) Process (K=4) Labor Output Labor Output Labor Output Output Produced Produced Produced Labor Produced 0 0 25 I 50 1 90 1 120 2 50 2 100 2 150 2 180 3 70 3 130 3 180 3 220 4 88 4 150 4 200 4 240 5 103 5 160 210 250 115 6 165 6 210 6 255 7 125 7 168 7 200 7 230 132 170 190 200 136 170 180 170 10 138 10 168 10 175 10 140 a. What is the marginal product of hiring the 8- and 9 worker, when the firm rents 2 units of capital? If this company is only interested in maximizing output, should this company hire 8 or 9 units of labor? Explain. b. In this case, should the firm hire one additional worker, that is the 10 unit of labor? Explain. Production in the Long-Run 4. Suppose that Jack can hire workers for $12 per hour or rent capital for $7 per hour. a. Write an expression for Jacks total cost as a function of how many workers he hires and how much capital he employs. b. Assume Jack wishes to hold their total costs to exactly $100. Use the expression in (a) to find the equation for an isocost line corresponding to exactly $100 of costs. Rearrange your equation to isolate capital. C. Graph the equation for the isocost line, putting labor on the horizontal axis and capital on the vertical axis. d. What is the vertical intercept of the line you drew? The horizontal intercept? What does each represent? e. What is the slope of the line you drew? What does it represent? f. Suppose that bargaining with the local labor union raises wages. Jack must now pay $14 per hour. What happens to the isocost line corresponding to $100 of expenditure? Explain. Show the new isocost line on your graph. 5. Baldor measures the marginal rate of technical substitution (MRTS) at - MPg MPA = -3. The prices of labor and capital faced by Baldor are such that - = -4. Is Baldor minimizing costs? Explain. ove its company situation?The following table shows real GDP (in 2012 Dollars) for Japan from 2012 to 2018, along with the population in each year. a) Calculate real GDP per capita for each year. Instructions: Complete the real GDP per capita column in the table below. Enter your responses rounded to the nearest whole number. Real GDP Population Real GDP Per Annual Growth Rate (Billions of 2012 (Millions of Capita (2012 (round to 2 Year Dollars ) People) Dollars) decimal places) 2012 $4,731 127.6 $ 2013 $4, 825 127.3 2014 $4, 843 127. 1 2015 $4,909 127.0 2016 $4,956 127.6 $ 2017 $5, 042 126.7 2018 $5, 099 126.4 $ b) Is Japan's population rising or falling? ( (Click to select) * c) In what year did real GDP per capita rise by the biggest percentage? O 2012 O 2014 O 2016 O 2017 O 2018d) By what percentage did GDP per capita change from 2012 to 2018? Instructions: Round your answer to two decimal places. % Plot real GDP per capita on a graph. INSTRUCTIONS: Use the plotting tool to plot GDP per capita. (7 points) GDP per Capita, Japan Real GDP (000) Tools 41 line 1 40 39 38 37 36 2017 2018 2019 2020 2011 2012 2013 2014 2015 2016 YearsThe following table shows data on consumption, investments, exports, imports, and government expenditures for the United States in 2016, as published by the Bureau of Economic Analysis. All figures are in billions of dollars. Fill in the missing cells in the table to calculate GDP using the expenditure approach. Data ( Billions of dollars) Consumption (C) 12,757.9 Investment (1) 3,035.7 Exports (X) 2,232.4 Imports (M) 2,733.7 Net Exports of Goods and Services Government Purchases (G) 3,276.7 Gross Domestic Product (GDP)