Suppose there are the following random variables:

X1: a normal random variable with = 1 and = 1 (you know this variable exists, but you do not have data on it)

Z: a normal random variable with = 1 and = 1

X2 = (X1+Z) / 2

e: a normal random variable with = 0 and = 1

Y = 10 + 5 X1 + 2 X2 + e

(a) Find the covariance of X2 and Y

(b) Find the variance of X2

(c) Suppose you do not have data on X1, so to estimate the impact of X2 on Y , you use the single variable regression Y = 0 + 1X2 + e What would be the expected value of 1? How would that compare to the impact of X2 on Y holding X1 constant?

(d) If you were to use Z as an instrumental variable for X2, what would be the first stage regression? Find the expected value of the slope and intercept for that first stage regression.

(e) What would be the second stage regression? Suppose the estimated slope and intercept from the first stage regression were exactly equal to the expected values you computed in the previous question. What would be the slope in the second stage regression?

QUESTION 5 The value added for Cookieinc is: $15,000 $25,000 $30,000 $35,000 QUESTION 6 The GDP for this economy is: C$70,000 $85,000 $100,000 C$115,000 QUESTION 7 The government expenditure in this economy is: $12,000 C $5,000 C $3,000 C $0 QUESTION 8Econ 178-001 International Trade Problem Set 5 Spring 2019 Please answer the following questions on separate sheets of paper. One of the questions will be randomly graded. The rest of the assignment will be "graded" for completeness. See syllabus for more details. 1. Using the short-run specific factors model, consider a situation where a country discovers a new technology that increases the amount of arable land it has for production. Assume that land is specific to food and cannot be used for clothing. a. In a diagram of the labor market, show what would happen to the amount of labor in each industry, the nominal wage and the real wage in terms of each good. Explain why the curve shifts in this way. b. Clearly explain what would happen (and how you know what happens) to the real return of capital and the real return on land. 2. Answer the following question under the assumptions of the Heckscher-Ohlin model. There are two industries of production: clothing (Qc) and food (QF). Clothing is capital-intensive and food is labor-intensive. There are two countries: Home and Foreign. Home is capital abundant and Foreign is labor abundant. (Same as in class) a. Draw a "box" graph that represents the labor and capital inputs into each industry in Home. b. What do the slopes of the lines drawn in part (a) represent? C. Now imagine the labor leaves the Home country. Show the effect either in part (a) above or redraw your graph. d. What happens to the production of each good in the economy? On a related noted, what happens to the amount of labor and capital used in each industry because of the change? e. What happens to real rent and real wages? 3. Draw a figure of the world labor market comparing the Home and Foreign wages (like the one we did in class). a. Imagine that without open borders for labor, the Foreign wage is higher that the Home wage. Mark this point on your graph with an L", w*s, and w* H. b. Imagine that immigration is allowed, but only half of those that would like to immigrate are able to do so. Draw the effect that this would have on the world market. Mark the new outcomes with an ("*, w* *, and WH- c. Identify the areas of your graphs that illustrate the gains to the Home and Foreign countries because of immigration. Explain why each of these areas lead to net benefits for each party.4. All goods in an economy are classified as agriculture (good 1) and manufacturing (good 2). These data are available for a country in the cases of autarky and of free trade. Price at Exports Imports Production Production autarky under free under free under under free trade trade autarky trade good 1 2 100 20 300 320 good 2 10 20 50 150 140 Calculate the gains from free trade, as the change to the welfare from autarky to free trade evaluated at autarky prices. Report the gains from free trade as a percentage of initial GDP (ie. total expenditures at autarky).consider the following graph. The world market price under free trade is $6. 15 Price S Austria A b C 6 D Quantity 9 12 18 24 27A manager randomly selected 24 large cash transactions at a bank that were made in January. The manager then carefully tracked down the details of these transactions to see that the correct procedures for reporting these large transactions were followed. This bank typically makes 1,200 such transactions monthly. (a) Is it appropriate to use a binomial model in this situation? (b) If the chance for a procedural error is 10%, is it likely that the auditor finds more than 2 such transactions? For this component, argue informally, without computing the probability, from the characteristics of the binomial model. (c) Find the probability in part b