Question 3: Price Dynamics Consider the following simple model analyzed in Lecture 4. Demand quantity: q =a; P1 xp Supply quantity: q =ay+p, Xp Equilibrium: q = Solving for the equilibrium price, we have p* = ;i;;Z' a 0 Let's assume as did in the lecture that only the supply side of the market is subject to unpredictable production shocks. Suppose there is a supply shock that reduces the production quantity in the first period from the equilibrium level. Let's assume that the producer determines the production quantity next period based on today's price. Hence the production quantity and the price will adjust over time according to the diagram below. Supply Demand Supply Shock a) b) c) d) e) a; 93 q* 9 9 What does this model imply about the price dynamics for the market? Write down the price dynamic formula and indicate the corresponding sign for the parameters. Now examine the U.S. lamb market using the data provided in the excel file \"Data Set for Assignment 1\". The file contains data on U.S. lamb prices, monthly averagefeeder lambs 60-90 Ibs. (S/cwt.) from January 1990 to December 2021. Plot the time series data on lamb prices. Calculate the descriptive statistics for the data series. Detrend the price data and produce the time series plot for the detrended price series. Calculate the autocorrelation and partial autocorrelation for the detrended lamb prices in (c) above withlag k=1, 2, 3, ...10. (Ignore stationarity issues, if any. What does your analysis in d) imply the price dynamics of the U.S. lamb market? In particular, is the assumption that \"the producer determines the production quantity next period based on today's price\" consistent with your analysis