Concept explainers
Use the elimination method in Exercises 55 – 58 to find an equilibrium point for the described supply-demand situation. You may assume that the supply and demand equations are both linear.
Supply and demand-housing. In doing a low-income housing survey, the local chamber of commerce found that if an apartment rents $400 per month, there were only 275 available; however, when the rental price rose to $550 per month, the supply increased to 350. In contrast, at a rental price of $400 per month, there was a demand for 450 units, but when the rental price increased to $550 per month, the demand dropped to only 200 units. Find the monthly rental price at which the number of apartments demanded and the number of apartments supplied will be equal.
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MYLAB MATH WITH PEARSON ETEXT FOR MATHEM
- Q. Table provided gives data on gross domestic product (GDP) for the United States for the years 1959–2005. a. Plot the GDP data in current and constant (i.e., 2000) dollars against time. b. Letting Y denote GDP and X time (measured chronologically starting with 1 for 1959, 2 for 1960, through 47 for 2005), see if the following model fits the GDP data: Yt = β1 + β2 Xt + ut Estimate this model for both current and constant-dollar GDP. c. How would you interpret β2? d. If there is a difference between β2 estimated for current-dollar GDP and that estimated for constant-dollar GDP, what explains the difference? e. From your results what can you say about the nature of inflation in the United States over the sample period?arrow_forwardThe figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. Use the information in the figure to solve Exercises 67–72. 35,000 30,000 C(x) = 10,000 + 30x 25,000 20,000 15,000 R(x) = 50x 10,000 5000 100 200 300 400 500 600 700 Radios Produced and Sold 67. How many radios must be produced and sold for the company to break even? 68. More than how many radios must be produced and sold for the company to have a profit? 69. Use the formulas shown in the voice balloons to find R(200) – C(200). Describe what this means for the company. 70. Use the formulas shown in the voice balloons to find R(300) – C(300). Describe what this means for the company. 71. a. Use the formulas shown in the voice balloons to write the company's profit function, P, from producing and selling x radios. b. Find the company's profit if 10,000 radios are produced and sold. 72. a. Use the formulas shown in the voice balloons to write the company's profit function,…arrow_forwardInsurance Rates The following table gives themonthly insurance rates for a $100,000 life insurancepolicy for smokers 35–50 years of age.a. Create a scatter plot for the data.b. Does it appear that a quadratic function can beused to model the data? If so, find the best-fittingquadratic model.c. Find the power model that is the best fit for the data.d. Compare the two models by graphing each modelon the same axes with the data points. Whichmodel appears to be the better fit?arrow_forward
- Solve the systems in Exercises 11–14.arrow_forwardIn Exercises 65–68, find and sketch the domain of ƒ. Then find an equation for the level curve or surface of the function passing through the given point.arrow_forwardSuppose the market demand for mangoes in the Sultanate of Oman is given by Qd = 300 – 20 P and the market supply for mangoes is given by Qs = 20 P – 100, where P = price (per kg mangoes). Graph the supply and demand schedules for mangoes using $5 through $15 as the value of P. In equilibrium, how much mangoes would be sold and at what price? What would happen if suppliers set the price of mangoes at $15? Explain the market adjustment process.arrow_forward
- The Internal Revenue Service Restructuring and Reform Act (RRA) was signed into law by President Bill Clinton in 1998. A major objective of the RRA was to promote electronic filing of tax returns. The data in the table that follows show the percentage of individual income tax returns filed electronically for filing years 2000–2008. Since the percentage P of returns filed electronically depends on the filing year y and each input corresponds to exactly one output, the percentage of returns filed electronically is a function of the filing year;so P(y) represents the percentage of returns filed electronically for filing year y. (a) Find the average rate of change of the percentage of e-filed returns from 2000 to 2002. (b) Find the average rate of change of the percentage of e-filed returns from 2004 to 2006. (c) Find the average rate of change of the percentage of e-filed returns from 2006 to 2008. (d) What is happening to the average rate of change as time passes?arrow_forwardExercises 93–94: Energy The following graph shows U.S. Energy consumption. 400 350 300 250 200 150 100 50 04 1970 1990 2010 Year 93. When was energy consumption increasing? 94. When was energy consumption decreasing? Energy (millions of Btu)arrow_forwardIn 2010, MonsterCollege surveyed 1250 U.S.college students expecting to graduate in the next several years.Respondents were asked the following question:What do you think your starting salary will be at your firstjob after college?The line graph shows the percentage of college students whoanticipated various starting salaries. Use the graph to solveExercises 9–14. What starting salary was anticipated by the greatestpercentage of college students? Estimate the percentage ofstudents who anticipated this salary? What starting salary was anticipated by the least percentageof college students? Estimate the percentage of students whoanticipated this salary? What starting salaries were anticipated by more than 20% ofcollege students? Estimate the percentage of students who anticipated astarting salary of $40 thousand.arrow_forward
- IKEA has a contract to deliver 100, 250, 190, 140, 220, and 110 home windows over the next 6 months. Production cost (labor, material, and utilities) per window varies by period and is estimated to be $50, $45, $55, $48, $52, and $50 over the next 6 months. To take advantage of the fluctuations in manufacturing cost, IKEA can produce more windows than needed in a given month and hold the extra units for delivery in later months. This will incur a storage cost at the rate of $8 per window per month, assessed on the end-of season inventory. Now IKEA wants to minimize their respective cost. Based on this data answer the following questions Qus.1)Write down the objective function of the linear programming consistent with the objective of IKEA.arrow_forward[For Q4 – Q5] Consider the following lifecycle model of consumption. Minjoon has 50 years of life remaining. He plans to work 30 more years from now and then retire. He earns $1,000 per year while he is working and has $200 per year pension income after retirement. He currently has $1,000 of savings. He wants equal consumption every year. The interest rate is zero. Q4. What will be Minjoon's wealth at the moment of retirement? Answer: a) $1,000. b) $3,000. c) $5,000. d) $10,000. Q5. Which of the following statements regarding this lifecycle model is (are) correct? I. If the income while working increases from $1,000 per year to $1,100 per year, Minjoon's optimal consumption before retirement will increase by $60 per year. II. Minjoon will decrease his consumption at the moment of retirement because he will have less income after his retirement. Answer: a) None of the above. b) I only. c) II only. d) I and II.arrow_forwardexercise #25arrow_forward
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