1. Suppose that we are interested in measuring the relationship between hourly wage and output productivity in the U.S economy. Variables hrwage(t) and outphr(t) denote the average hourly wage and output productivity in the U.S economy for year t. We start by estimating the model specification shown in equation (1) below: log(hrwage) = Bo+B₁ log(outphr₂) + ut. where log(.) denotes the natural logarithm and ut is the error term. (a) Provide a brief interpretation of parameters 0 and 1 in (1).
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- 7 Suppose the following model describes the relationship between annual salary (salary) and the number of previous years of labor market experience (exper): log(salary) = 10.6 + .027 exper. (i) What is salary when exper = 0? When exper = 5? (Hint: You will need to exponentiate.) (ii) Use equation (A.28) to approximate the percentage increase in salary when exper increases by five years. (iii) Use the results of part (i) to compute the exact percentage difference in salary when exper = 5 and еxper = 0. Comment on how this compares with the approximation in part (ii).If the annual rate of world oil consumption t years after 1970 is modeledby the equation R(t) = 16.1e^.07t (billions of barrels per year), how much total oil (net change) was used between 1976 and 1980?Colton is trying to figure out when two buses traveling at different speeds will pass one another. The buses are traveling in the same direction and begin 3 miles apart. He has defined variable tt as follows: Let tt represent the time in hours. Is this a good variable definition? YES OR NO ? IF NO than explain why?
- Anation with fixed quantities of resources is able to produce any of the following combinations of carpet and carpet looms: Yards of Carpet (Millions) Carpet Looms (Thousands) 75 60 20 45 35 30 45 15 50 50 These figures assume that a certain number of previously produced looms are available in the current period for producing carpet. To answer this question, assume carpet looms is on the y-axis and yards of carpet is on the x-ais The plot of these points that make up the PPF has a vertical intercept of and a horizontal intercept of This PPF would be (Enter your responses as a wvhole number) bowed out a straight lineQ5. Make a hypothetical data table and try to make interrelationships between AC, MC and AVC for ten observations. Keep in mind the trend of certain variables. Support Your answer with the help of correct graphs and their respective interpretations like Q TFC TVC TC ATC AVC AFC MC 1 2 3 4 And So onConsider the two-sector macroeconomic model of a fictitious country: dy dt C = 0.5 Y + 540 I = 425 Where C = consumption; I = investment and Y = national income. = 0.034(C+I - 0.6 Y) Determine the following: (a) If Y(0) = 14,000, find an expression for Y (t) by solving the differential equation. (b) Find the time taken for income to fall to 13,000. (c) Is the system stable or unstable? Explain your answer.
- C. Suppose your neighbor is a physics major who also races motorcycles, and she tells you that horsepower can be expressed in terms of the following equation: H = MDA/S where M=mass, D-distance, A=acceleration and S and H are as defined above. Based on this conversation with your neighbor, you decide to change the functional form of the relationship to include 1/H rather than H as an explanatory variable because that's the appropriate theoretical relationship between the two variables. Estimate the above equation, substituting 1/H for H. Which of the two models do you prefer and why?George Kyparisis makes bowling balls in his Miami plant. With recent increases in his costs, he has a newfound interest in efficiency. George is interested in determining the productivity of his organization. He would like to know if his organization is maintaining the manufacturing average of a 3% increase in productivity. He has the following data representing a month from last year and an equivalent month this year: Resin Productivity Change if necessary). The productivity change for each of the inputs (Labor, Resin, Capital, and Energy) is: Labor Productivity Change = if necessary). = Units Produced Labor (hours) Resin (pounds) Capital Invested ($) Energy (BTU) Last Year 1,200 300 60 10,000 2,900 Energy Productivity Change = if necessary). Now 1,200 250 46 11,000 2,750 % (enter your response as a percentage rounded to two decimal places and include a minus sign % (enter your response as a percentage rounded to two decimal places and include a minus sign Capital Invested…1. Suppose that an equation for infant mortality is described by the function: - VD (P)1². where i is the infant mortality rate (expressed in per 1,000 children), Y is the gross domestic product (in US dollars), P is the population, and 3 and b are constants. a. Derive a linear (in parameters) equation from the function above with In i as the left Y -hand side variable and In y on the right-hand side. Note that y =, which is the P' GDP per capita. b. Identify the slope and intercept in the derived equation in (a). What could be the relationship between i and y? Provide an economic explanation. c. Derive a formula of the slope parameter in the linear equation in (a) for the interpretation of the changes in the variables. Interpret the resulting equation.
- Given the following: C(YT) = 200+ 0.75(Y-T) I(r) = 80-20r L(r,Y)=Y-90r G = 200 T = 75 M = 2500 P = 4 a) What is the exact expression for the IS curve (express Y in terms of r)? b) What is the exact expression for the LM curve (express Y in terms of r)?With respect to a given product, describe the connection that exists between equalibrium/disequalibrium and prediction. cite an unique examplei) C = 250 + 0.8 Y I = 150G = 300TR = 100NX = 100t =0.25 ii) C^ falls to 50, MPS falls to .05, I falls to 10, G falls to 100 and NX falls to 10. Make a graph of i) and ii)