Provide solutions for the following attachments.

Use the willingness-to-pay information about the buyers (Ariel, Bridget, and Connie) and the willingness-to-accept information about the sellers (Daniel, Etienne, and Franklin) below to construct a "stepped" demand and supply diagram like this one from my notes on Unit #7. (You'll also have one question to answer below.) Willingness-To-Pay information Ariel Bridget Connie willingness-to-pay $5 $7 $9 for the 1 widget willingness-to-pay $4 $6 $7 for the 2" widget willingness-to-pay $3 $4 $5 for the 3 widget willingness-to-pay $2 $3 $4 for the 4 widget willingness-to-pay $1 $2 $3 for the 5" widget Willingness-To-Accept information A Daniel Etienne Franklin willingness-to-1. We use the added variable technique to derive the variance ination factor (VIP). Consider a linear model of the form 91' =50+l31$1+l3213922+-"+}3p$a'p+zr, 5'3: 1:"'ana (1) where the errors are uncorrelated with mean zero and variance 02. Let X denote the n X p' predictor matrix and assume X is of full rank. We will derive the VIP for ip. The same derivation applies to any other coefcient simply by rearranging the columns of X. Let U denote the matrix containing the rst p' 1 columns of X and let z denote the the last column of X so that X = [U 2]. Then we can write the model in (1) as 50 x91 Y=[U z](,:J)+t-:=Ua+z6p+e with a: (2) x810. 1 Let 2 denote the vector of tted values from the least squares regression of z on the columns of U (Le. the regression of X.p on all the other variables), and let T : z 2 denote the residuals from that regression. Note that 'r' and 3 are not random, they are constant vectors obtained by linear transformations of z. (a) Show that the regression model in (2) can be rewritten in the form for some constant vector 6 of the same length as a. (Hint: z : i l 'r and 2? = U(UTU)_1UTz). (b) Show that UT? 2 0, a zero vector. (0) Obtain simplied expressions for the least squares estimators of 5 and 5?, showing, in particular, that 5,, : 'rTY/rT'r. (d) Based on Part (c) and the model assumptions, show that 0.2 ELK\"? _ is)? where :Eg-p is the LS tted value from regression X,D on the all the other predictor variables with an intercept. var(,p) : What Is Fiscal Policy? Government budget constraint Bt - Bt-1 = rBt-1 + Gt - It deficits in year t interest payments primary deficit Bt = (1+r) Bt-1+ Gt - Tt Some remarks deficit (flow, Bt - Bt-1) v.s. debt (stock, Bt) evolution of debt-to-GDP ratio Bt Bt-1 Gt - Tt = (r -g) Bt-1 + Yt-1 Yt-1 Y+ change in debt ratio initial debt ratio primary deficit ratio Fiscal policy (changes in (Gt, Tt) to achieve macro objectives) v.s. automatic stabilizer