The Vista TV Cable Co. currently has 100,000 subscribers who are each paying a monthly rate of $40. A survey reveals that there will be 1000 more subscribers for each $0.25 decrease in the rate. At what rate will maximum revenue be obtained, and how many subscribers will there be at this rate?
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- The demand function for SkanDisc 2GB thumb drives is given by p- 4(x + 3) e"/a where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Compute the price, p, when x 6. Do not round your answer. Price, p- 36e dollars Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x- 6. Do not round your answer. Rate of change of demand, x' x thousands of units per dollar Compute the elasticity of demand when x - 6. Do not round your answer. Elasticity of Demand-For the demand equation, express the total revenue R as a function of the price p per item. q=-5p+1000 R(p) = Sketch the graph of the resulting function. O No Solution Help 20 90000 80000 70000 60000 50000 40000 30000 20006 10000 20 40 60 50 100 120 140 160 180 200 220 240 260 280 -1/000+4 51 WebAssign. Graphing Tool Determine the price p (in dollars) that maximizes total revenue. p = $ Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties.The chart below shows how annual electricity for an average Ontario household would vary with the price paid for electricity. Calculate the arc elasticity of demand for electricity for this average houschold. Also, in the final column, calculate the total revenue from sales of clectricity to this household. Price Quantity Demanded Kwh/year Total Revenue $/kwh Elasticity of Demand $0.25 1200 -0.36 $0.20 1300 $0.15 1400 $0.10 1500 $0.05 1600 Hint: The own price elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in the price. What factors do you think influence the elasticity of demand for this household?
- On the following graph, use the green point (triangle symbol) to plot the annual total revenue when the market price is $40, $60, $80, $100, $120, $140, and $160 per bike. 6250 5820 Total Revenue 5390 4960 4530 4100 3670 3240 2810 2380 20 40 60 80 100 120 140 160 180 200 220 240 PRICE (Dollars per bike) According to the midpoint method, the price elasticity of demand between points A and B is approximately Suppose the price of bikes is currently $80 per bike, shown as point A on the initial graph. Because the demand between points A and B is , a $20-per-bike decrease in price will lead to in total revenue per day. In general, in order for a price increase to cause an increase in total revenue, demand must be TOTAL REVENUE (Dollars)6. Elasticity and total revenue The following graph shows the daily demand curve for bikes in Chicago. Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve. Note: You will not be graded on any changes made to this graph. 120 110 Total Revenue 100 90 80 70 60 40 A 30 20 10 Demand 16 24 32 40 48 56 64 72 80 88 96 QUANTITY (Bikes) PRICE (Dollars per bike) 50he quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $136. The quantity demanded ach month is 1000 when the unit price is $106. The suppliers will market 750 espresso makers when the unit price is $80 er higher. At a unit price of $100, they are willing to market 2250 units. Both the supply and demand equations are known o be linear. (a) Find the demand equation. -1 -x + 146 25 p = (b) Find the supply equation. 1 x+ 70 p = 75* (c) Find the equilibrium quantity and the equilibrium price. |× units
- 4. You have been hired as a consultant to estimate the demand for various brands ofcoffee in the market. You are provided with annual price data for two years by U.S.state and the quantities sold. You want to estimate a demand function for coffeeusing this data. What problems do you think you will encounter if you estimatedthe demand equation by OLS?Determine the revenue per year and revenue over the lifetime of the customer Number of smart devices over first half of life Number of smart devices over second half of life Average $ transaction per device $ monthly subscription paid - monthly total Average annual revenue -first half of life Average annual revenue -second half of life Average life of subscribed customer Revenue over lifetime Minimally Satisfied 2 1 $79 $9.99 2 years Moderately Satisfied 4 2 $85 $19.99 5 years Highly Satisfied 6 3 $79 $19.99 7 yearsThe price elasticity of demand for a product is estimated to be -2.3. At the initial price of $20, the quantity demanded was 10 units. If the firm increases theprice to $22.50, quantity demanded is expected tobyO A. decrease: 28.75%6O B. increase; 12.596O C. decrease: 18.75%O D. increase: 17.2596
- 6. Elasticity and total revenue The following graph shows the daily demand curve for bikes in Denver. Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve. Note: You will not be graded on any changes made to this graph. 2 Total Revenue PRICE (Dollars per bike) 88NR S 89 88 89 O 300 275 18 27 35 45 54 53 72 QUANTITY (Bikes) 91 Demand 90 99 108The figure below represents the weekly demand for GPS units. Price (dollars) 220 200- 180- 160 140 120 100- 80 60 40 20 0 Demand for GPS Units 40 80 120 160 200 240 280 320 360 400 440 Quantity (GPS units) < Prev ***Y 3 of 18 +++ www Next MaternitCreative Homework/Short Project Assume that you arean entrepreneur who runs a bakery that sells glutenfree breads and cakes. You believe that the currenteconomic conditions merit an increase in the price ofyour baked goods. You are concerned. however, thatincreasing the price might not be profitable becauseyou are unsure of the price elasticity of demand for yourproducts. Develop a plan for the measurement of priceelasticity of demand for your products. What findingswould lead you to increase the price? What findingswould cause you to rethink the decision to increaseprices? Develop a presentation for your class outlining(I) the concept of elasticity of demand, (2) why raisingprices without undetstanding the elasticity would bea bad move. (3) your recommendations for measurement. and (4) the potential impact on profits for elasticand inelastic demand