please answer the following questions!
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1. (70 points total (+10 point bonus opportunity)) Awesome Apples Orchard sells tree fruit at farm markets. Based on their years of sales experience, the owners have mapped the demand for apples in the table below, where Price is in $/box (2 lbs) and Quantity refers to boxes of apples sold daily. In particular, they have learned that the Demand for Apples (holding constant other factors) takes the form: QA = 300 - 30PA a. (20 points) For your marketing analysis, please complete the table below. Use the point elasticity formula and calculate marginal revenue with respect to change in price. For Marginal Revenue, AQ/AP, and P/Q, please compute changes between the row above and the current row. (The 40/AP and P/Q columns are for your convenience and will not be graded.) Marginal Revenue = dTR/do. Price Quantity Total Marginal 40/AP P/Q Own price ($/box) (boxes/day) Revenue revenue (not (not graded) point ($/day) (ATR/AP) graded) elasticity E(Q.P) 10 0 9 30 8 60 90 6 120 5 150 4 180 WJ 210 2 240 270 0 300[15 points} Suppose the demand function for Awesome Apples appears below, where P; is price of Apples and Pp is price of Fears: of: = soo- son. + so. i. What is the relationship between apples and pears in this market ii; are they substitutes or complements}? Explain. ii. Suppose the company has been selling 13!} boxes per day of apples at a price of apples of 55mm with a pear price of 53%. If the price of pears rises to 59mm, 1. What happens to the quantity of apple boxes sold? 2. What is the point cross elasticity of demand for apples with respect to the prioe of pears under the initial condition when price of pears is 53mm? {Rou nd answer to 1 decimal places] 3. Is the cross-price elasticity of demand for Awesome Apples with respect to the price of pears elastic or inelastic? Why? b. [15 points; and If) glut bonus Jfgraphs are mode on Excel} Make two graphs, one directly below the other [so you can compare]: [Remember to label curves, label axes with variables and units of measure, and indicate intercepts and other defining points [like maximum or minimum points].] i. In the upper chart, graph the inverse Demand curve for Apples. ii. In the lower chart, using Quantity across the horizontal axis {with identical spacing to the upper chart}, graph Total Revenue from Apple sales. c. [9 points} What is the relationship between total revenue, marginal revenue, and own price elasticity of demand for Awesome Apples?I [Remember that Marginal Revenue in response to Price here is measured between the upper and current rows in the table above, not just on the current row.] d. [9 points} If you knew only the own prioe elasticity of demand for Awesome Apples and you had the power to set your price, how could you use that elasticity to pick the price that will maximize total revenue? What prioe would you choose, and what quantity of sales would you expect as a result? 2. (14 points) Consumer and Producer Surplus a. Define Consumer Surplus, explaining what makes it "surplus" to consumers. b. Illustrate Consumer Surplus in the figure below. Label any relevant prices and quantity values. c. Define Producer Surplus, explaining what makes it "surplus" to producers. d. Illustrate Producer Surplus in the figure below. S Price D Quantity3. (16 points) Excise tax An excise tax is a tax at a fixed rate per unit of the good for sale. For example, Michigan's gasoline tax is an excise tax of 18.7 cents per gallon. Unlike an ad valorem tox, an excise tax is not a percentage; it is a fixed amount per unit. a. Draw an example of an excise tax on the graph below. Label any relevant prices and quantity values. b. How does such a tax change the market equilibrium i. Price to consumers? ii. Price to producers? ii. Quantity to consumers? iv. Quantity to producers? S Price D Quantity
