0.1 Introduction to Mathing with R - Practice Solving a System of Equations: Supply and Demand Given the following (inverse) supply and demand functions: P = 10Qd P = Q2s Solve for the equilibrium price and quantity using nleqslv::nleqslv. R Code equilibrium_price < - sol$x[ - 1] Graph the market equilibrium. Scale the x and y axes from 0 to 5 and 0 to 10, respectively. Add a point and label with the equilibrium values. R Code
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- a. Graph the points of these supply and demand curves for orange juice. Be sure to put price on the vertical axis and quantity on the horizontal axis. b. Do these points seem to lie along two straight lines? If so, figure out the precise algebraic equation of these lines. (Hint: If the points do lie on straight lines, you need only consider two points on each of them to calculate the lines.) c. Use your solutions from part b to calculate the "excess demand" for orange juice if the market price is zero. d. Use your solutions from part b to calculate the "excess supply" of orange juice if the orange juice price is $6 per gallon.Suppose that the annual demand and supply curves for some good in a competitive market are QD = 26 – 2P and QS = −2 + 2P a: Solve for the equilibrium quantity and price.b: Neatly graph this market, showing the horizontal and vertical intercepts of the demand curve,the vertical intercept of the supply curve, and the equilibrium. Make sure to put quantity on the horizontalaxis.Suppose the supply of a good is given by the equation Q = −6+2P and the demand for the good is given by the equation QD = 14 - 2P, where quantity (Q) is measured in millions of units and price (P) is measured in dollars per unit. The equilibrium quantity in this market is 4 million PRICE (Dollars per unit) the following graph, plot the demand curve using the blue line (circle symbol) and plot the supply curve using the orange line (square symbol). Then place the black point (plus symbol) at the equilibrium price and quantity. Dashed drop lines will automatically extend to both axes. 10 9 8 7 2 1 0 0 1 2 3 4 5 6 7 QUANTITY (Millions of units) 8 units and the equilibrium price is 9 10 Demand Supply $5. Equilibrium
- ....... Problem 03-09 (part b) Suppose the price of grapefruit falls drastically. Instructions: Depict how this event will affect the market for oranges by dragging the appropriate curve in the graph. 1 Market for oranges Price ($/orange) P* Q* Quantity (oranges/week) demand E2. Given the demand and supply function: S= 100 + 20P D = 150 - 10P a. Compute for the equilibrium price and equilibrium quantity. b. Illustrate the equilibrium condition graphically.The demand for coffee is given by the following equation, where QD�� stands for the quantity demanded and P stands for price. QD=100−4PQD= 100- 4P The supply of coffee is given by the following equation, where QS�� stands for the quantity supplied and P stands for price. QS=-10+2PQS= -10+ 2P For parts a-d, consider a graph of the demand and supply curves with price on the vertical axis and quantity on the horizontal axis. What is the slope of demand? Slope = At what price is quantity demanded equal to zero (this is, graphically, the vertical intercept of Demand)? P = What is the slope of supply? Slope = At what price is quantity supplied equal to zero (this is, graphically, the vertical intercept of Supply)? P =
- Suppose that the market for bottled water can be represented by the following equations: Demand: P = 10 - 2QDSupply: P = 1 + 0.5QSwhere P is the price per gallon, and Q represents quantity of purified water, represented inmillions of gallons of water consumed.a) Calculate the equilibrium price and quantity of bottled water.b) Concerned over high water prices after the winter storm, the government sets a priceceiling of $2.25 per gallon of water. What is the new quantity of water sold in themarket? Use supply and demand curves to illustrate your answer, showing both theoriginal equilibrium from part a) and the new quantity sold with the price ceiling.c) Calculate the producer surplus and consumer surplus at the initial equilibrium priceand quantity from part a).d) Calculate the new producer surplus and consumer surplus with the price ceiling frompart b).e) How does the total consumer and producer surplus in part c) compare to the totalconsumer and producer surplus in part d)? What…Suppose a war breaks out in the Middle East, where a large proportion of the world's oil production takes place. Answer the following questions using supply-and-demand graphs. How will the market for used SUVs be affected? How do the equilibrium price and quantity change? Is there any ambiguity in the change in equilibrium price and/or equilibrium quantity?Suppose that Carlos and Deborah are the only suppliers of pieces of cake in some hypothetical market. Their annual supply schedules are given by the following table: Carlos's Quantity Supplied Deborah's Quantity Supplied (Pieces) ITT 20 30 35 40 PRICE (Dollars per piece) (Dollars per piece) 5 Price 0 0 1 2 3 4 5 20 On the following graph, plot Carlos's supply of pieces of cake using the green points (triangle symbol). Next, plot Deborah's supply of pieces of cake using the purple points (diamond symbol). Finally, plot the market supply of pieces of cake using the orange points (square symbol). Note: Line segments will automatically connect the points. Remember to plot from left to right. (?) 40 60 80 QUANTITY (Pieces) 100 (Pieces) 120 20 40 55 65 70 Carlos's Supply Deborah's Supply O Market Supply
- The city of Cedar Rapids has a large number of video poker arcades. The demand by patrons for the games (in thousands per week) is Qd = 180 - 4P and the supply is Qs = 2P - 30 where P is the price in cents charged to play a game. What is the equilibrium number (quantity) of games played? What is the equilibrium price? Draw a diagram depicting the equilibrium in this market.(d) Consider the following demand-supply model: P =15−Qd; P =3+Qs Use the equilibrium condition Qd=Qs=Q, and find the equilibrium price and quantity. Show this equilibrium in a graph. (e) What are definitional, behavioral, and conditional equations? Give examples.