.Provide adequate solutions to the following attachments.

Consider an economy with a representative consumer whose preferences are represented by the utility function:

U(c, l) = log c + ? log l

Consumer faces the budget constraint:

c = wNs + ?

and the time constraint:

l + Ns = h

where h > 0 is time endowment.

There is also a representative firm that uses technology: Y = zNd

(a) Write the consumer and firm's problem. Don't solve them yet.

(b) Define the competitive equilibrium.

(c) Solve consumer and firm's problem and find the competitive equilibrium. Check to make sure that all conditions required for a competitive equilibrium are satisfied. Now introduce a government that spends an amount G of consumption good financed through taxes.

(d) How does the definition of competitive equilibrium change?

(e) Suppose the government imposes lump-sum tax on the consumer. Solve the consumer and firm's problem and find the competitive equilibrium allocations and prices in this case.

(f) Formulate the planner's problem and solve for Pareto optimal allocations.

(g) Now suppose that the government imposes labor income tax to finance the government expenditure instead. In particular, the consumer's budget constraint changes to c = (1 ? t)wNs + ? Find competitive equilibrium allocations and prices in this case.

(h) If the government cared for the consumer's welfare, which tax regime would it choose? Why?

(i) Suppose the government chooses distortionary tax to finance G. Using the competitive equilibrium value for labor supply, write the revenue function for the government. Solve for tax rates that can finance G. If there are multiple tax rates what is the effect of using one vs. the other?

Question 1 Run in R the following lines of code: set.seed{63921) x=arima.sim(n=350, model=1ist{ar=c {0 . 7", O .2) ,ma=0. 357)] (a) Explain what each of theSe two lines instructions do in R. MarksES] (b) For the data vector x produced using arima . 3 im as above, generate: (a) The corresponding time series plot. Marks [3] (b) The corresponding ACF and PACF plots. Marks {4] (0) Fit to the data vector x, the following two models: (a) ARMA(2,2). Marks [3] (b) ARMA(2,1). Marks [3] {c} Which one of the two models above would you chose? Explain your reasoning. Marks [6] ((1) State the equation of the model that you chose in part (c) and perform some diagnostic testing by using the command t sdiag in R and by interpreting its output. Marks [10] (e) Show how can you perform in R the Ljung-Box test for the residuals as in formula 4.11 in the notes of the for lag 5:10. Marks {6] Homework 2 (Due: In class, Tuesday, 09/24/19) 1. a. A zero-coupon bond pays $1000 in five years. i) What is the value of the bond today? The nominal interest rate i is 3%. ii) Price the bond if the interest rate is now 7%. ili) Describe the relationship between the interest rate and the bond price. b. A zero-coupon bond pays $1000 in one year and sells for $920 now. Calculate the yield to maturity of the bond. c. A zero-coupon bond pays $1000 in six years and sells for $750 now. Calculate the yield to maturity of the bond to the nearest basis point (one hundredth of one percent). d. A consol pays $20 each year forever. The consol is currently selling for $160. The consol begins payments next year. What is the yield to maturity of the consol? e. A one-period coupon bond has a face value of SFV and pays an annual coupon amount C. Show that if the bond is priced at par (that is, the bond price equals its face value), then the yield of the bond is the coupon rate c. f. An annual coupon bond has a maturity of twelve years, a face value of $1000, and a coupon rate of 4%. The current market price of the bond is $780. Use a grid search to find the yield to maturity of the bond to the nearest basis point (one hundredth of a percent). Other methods will not receive full credit. Use a spreadsheet program and print a copy of your work. g. A U.S. Treasury note with a face value of $1000 pays interest semiannually at matures in three years. If the coupon rate is 4% and the bond equivalent yield is 5%, find the price of the note. Obey all pricing conventions. h. i) At the grocery store, apples cost 96 cents and bananas cost 92 cents. If a shopper buys twenty apples and ten bananas, what is the total cost at checkout? ii) A one year zero coupon bond with a face value of $100 has a yield of 4.1667%. A similar bond with a maturity of two years has a yield of 4.2572%. If a bond manager holds a bond portfolio with twenty zero coupon bonds that mature in one year and ten zero coupon bonds that mature in two years, what is the value of the bond portfolio? iii) Compare part (i) to part (ii) in a sentence or two. i. Consider the prices for the following zero-coupon bonds: Bond Maturity Face Value Price Bond A 1 year $1 0.98 Bond B 2 year $1 0.94 Bond C 3 year $25 23 Calculate the price of an annual coupon bond that matures in 3 years with a coupon rate of 5% on a face value of $100