A plant nursery in a regional town is known for its range of trees. One year the growing conditions are particularly good for trees, so the nursery ends up with too much stock. To clear this excess stock, the nursery reduces the average price of its trees by $15 per tree. Your task is to determine the consequences of the $15 price reduction.
The supply and demand equations are given by Demand Equation: 𝑝 = 150 − 10𝑎𝑞
Supply Equation: 𝑝 = 0.00001𝑞 2 + 2𝑏𝑞 + 20
where q is the number of customers (in hundreds per year) ; p is the price of a tree in dollars. a and b are coefficients to be chosen below.
Steps to complete to undertake the investigation
1. Obtain two random numbers for a and b between 0.1 and 0.9 inclusive. Use the Excel random function =Rand() or the RANDOM key on your calculator.
2. Find the equilibrium price and quantity algebraically, without the price decrease.
3. Update the demand equation to include the $15 price decrease.
4. Use algebra to find the new equilibrium price and quantity.
5. Use Excel to graph on the same set of axes, the original supply and demand equations (from part 1) and the updated demand equation with the proposed price decrease (part 3)
6. Use your results to complete the following summary table. Round answers to two decimal places, except for total revenue amounts which round to 0 decimal places Before price reduction After price reduction Difference Equilibrium quantity Equilibrium price: consumer pays Equilibrium price: restaurant would charge without any price reduction Revenue restaurant would receive without any price reduction Revenue restaurant receives with the price reduction LEAVE THIS CELL BLANK 7.
Summarise your findings in 300 words. In your conclusion: a. Discuss the effect of the surcharge on price, quantity and revenue b. Provide a recommendation to the nursery on whether to introduce the price decrease or not c. Note any assumptions you have made and any limitations of your findings.