Concept explainers
Find the equilibrium quantity and equilibrium price, and graph the following price-supply and price-demand equations:
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Additional Math Textbook Solutions
A Survey of Mathematics with Applications (10th Edition) - Standalone book
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Fundamentals of Differential Equations and Boundary Value Problems
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Probability and Statistics for Engineers and Scientists
- Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given. Supply: p= 45q Demand: p = -q + 10,000 The equilibrium quantity is q= at price p = $ .arrow_forwardAssume the yearly savings in gasoline costs due to the purchase of a hybrid auto- mobile are $400 and the extra cost of purchasing the hybrid is $4500. a. Produce an equation of net savings over a period of x years. b. Graph this equation on an appropriate rectangular coordinate axis system and identify the point that indicates the number of years required to break even. How long does it take to break even?arrow_forwardFind the equilibrium price and quantity for the supply in demand and equations. d(p)= 14,400-5p s(p)= 1,500+2parrow_forward
- A real estate office manages an apartment complex with 50 units. When the rent is $790 per month, all 50 units are occupied. However, when the rent is $834, the average number of occupied units drops to 46. Assume that the relationship between the monthly rent p and the demand x is linear. (Note: the term demand refers to the number of occupied units.) (a) Write a linear equation giving the demand x in terms of the rent p. x (p) = (b) Use a graphing utility to graph the demand equation and use the trace feature to predict the number of units occupied if the rent is raised to $845. units (c) Predict the number of units occupied if the rent is lowered to $823. Verify graphically. unitsarrow_forwardBased on the figure on the previous page, estimate as well as you can the coordinates of the four indicated points and write down two linear equations, one for the demand curve and one for the supply curve. Use P for price, QS for the quantity supplied, and QD for the quantity demanded.arrow_forwardThe demand and supply for the cleaning and grooming of a pet are given for two prices Demand Supply Price 680 815 105 780 735 85 a. Find the linear demand equation. b. Find the linear supply equation. c. Find the equilibrium price and quantity. d. Give the interpretation of the equilibrium point.arrow_forward
- A company produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is shown, where p is the price per unit in dollars and D is the demand per month. The company is seeking tomaximize its profit. The fixed cost is $1,000 per month and the variable cost (cv) is $40 per unit. Solve, a. What is the number of units that should be produced and sold each month to maximize profit? b. Show that your answer to Part (a) maximizes profit.arrow_forwardConsider the Honduran market for soybeans. The following graph shows the domestic demand and domestic supply curves for soybeans in Honduras. Suppose Honduras's government currently does not allow international trade in soybeans. Use the black point (plus symbol) to indicate the equilibrium price of a ton of soybeans and the equilibrium quantity or soybeans in Honduras in the absence of international trade. Then, use the green triangie (triangie symbol) to shade the area representing consumer surplus in equilibrium. Finally, use the purpie triangle (diamond symbol) to shade the area representing producer surpius in equilibrum. Domestic Supply 380 Domestic Demand 365 Equilibrium without Trade 350 335 320 Consumer Surplus 305 290 Producer Surplus 275 260 245 230 25 50 75 100 125 150 175 200 225 250 QUANTITY (Tans of saybeans) Based on the previous graph, total surplus in the absence of international trade is s PRICE (Dollars per ton)arrow_forwardAn employee has two options to consider for a position in a company. The first position pays $19.15 an hour plus an additional amount of $0.65 per unit produced per hour. The second position pays $13.75 an hour plus an additional amount of $1.25 per unit produced per hour. (a) Let x be the number of units produced per hour. For each option, state a linear equation for the hourly wage income Y in terms of x. (Note: Use lowercase letter x). Option 1: Y = Option 2: Y2 = (b) Graph the linear equations in part (a) and find the point of intersection. (х, у) %3D (c) Interpret the meaning of the intersection point from part (b). When Select-- + are produced per hour, the (-select--- +) for both options is $ per hour. (d) How would you use this information to select the correct option if the goal were to obtain the highest hourly wage? Choose [--Select-- if you think you will produce less than units per hour, and choose -Select-- if you think you will produce more than units per hour.arrow_forward
- Poverty incidence can be predicted using the linear equation Y=0.12+0.6558X , where Y refers to the poverty incidence and X refers to the proportion of the population (PHEAD) headed by a male married person who had reached at most secondary education. If PHEAD in province A decreased from 0.30 to 0.25, what is the predicted percentage increase or decrease in poverty incidence in province A?arrow_forwardFind the point of equilibrium for the demand and supply equations. Demand Supply p = 600 − 0.0004x p = 375 + 0.0005x x = units p = dollarsarrow_forwardThe Consumer Price Index (CPI), which measures the cost of a typical package of consumer goods, was 224.2 in 2011 and 233.2 in 2016. Let x = 11 correspond to the year 2011 and estimate the CPI in 2014 and 2015. Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then estimate the requested quantities. Let y represent the CPI. The linear equation that best models the CPI is (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning