1. 25 points During the course of the pandemic (2020-2021), the price of lumber (wooden planks etc.) has increased by about 50%. Before the pandemic contracts for delivery of one cubic meter of lumber traded on the US market at an average price of $250. During 2020-21 the average has been around $375 In general, a price increase could be due to an increase in demand, a decrease in supply, or both. Experts maintain that the reason for the price increase of lumber, is an increase in demand, not a decrease in supply (possibly be cause people have started more homerenovations instead of travel, which has been restricted during the pandemic). Let's assume that demand for lumber in the US depends on the price and total income income, as well as an umneasurable "taste\" factor. Total US income before the pandemic was $21 trillion, during the rst part of the pandemic income decreased by about $1 trillion (it has now recovered, but from the stand point of this question, we assume that it remained lower). Assume that the demand curve for lumber is given by 1 QD=a0-P+Y, where Q3 is billions of m3 of lumber, P is the price (in $) per m3, Y is total US income (in trillion $), and 0:0 is the \"taste\" factor. The supply function of lumber is: 1 S _. there 80 is a constant term in the supply function. (a) Assume that the equilibrium quantity Q\" in 2019 was 30 billion m3, and the equilibrium price was $250. Solve for on and 8,]. (b) Solve for the inverse supply and demand curves, given the income before the pandemic. Illustrate both curves in a single supply 35 demand diagram. (c) If the supply curve didn't change during the pandemic, and the price rose to $375, by how much did the quantity supplied increase? (d) Taking into account the decrease in income, solve for the new inter- cept of the direct demand curve (0:0). Derive an expression for the new inverse demand curve. Illustrate how the demand curve shifted in the same diagram as in b). (e) Calculate the own elasticity of demand around the initial equilibrium (pm-pandemic) and around the new equilibrium (pandemic). Com- ment on the differences in this measure between the two equilibria. Also calculate the average elasticiy of supply between the two equi- libria. From the standpoint of the demand and supply elasticities, what is the main reason why the price of lumber increased so much