solve the following c

Consider a simple utility function for two goods, x1 and x2: u = (x1 1) 1 (x2 2) 2 , with 1 > 0, 2 > 0. The parameters 1 and 2 are constants, but they could be positive or negative. (a) Someone suggests that "it would be okay" to assume that 1 + 2 = 1. Yet someone else claims that this restriction may be unrealistic. Which person is correct? Briefly explain your answer. (b) Suppose that the person with the above utility function is struck by lightning. He survives, except now his utility function is u = 1 log(x1 1) + 2 log(x2 2). Will his consumption decisions change as a result of being struck by lightning? Briefly explain your answer. (c) Returning to the original utility function, assume that the consumer faces the budget constraint p1x1 + p2x2 = w, where p1 > 0, p2 > 0 are prices and w > 0 is wealth. Set up the Lagrangean and solve for the two first-order conditions. Then use the budget constraint to solve for the Walrasian demands of both goods. These should be functions of p1, p2, w, 1, 2, 1, and 2. Finally, use your answer to part (a) to simplify your answer. (d) Finally, turn to a more general utility function with L goods: u = Y L k=1 (xk k) k , where k > 0 for all k, which is maximized subject to the budget constraint PL k=1 pkxk = w. Using the same approach as in part (c), derive the Walrasian demands for the L goods. (Hint: first substitute out the Lagrangean multiplier using the first-order conditions for two goods, i and j, then find an expression for pixi and sum that expression over all i, using a normalization similar to the one used in part (c)).

Consider an expenditure function that has the form log[e(p, u)] = X L k=1 k log(pk) + u Y L k=1 p k k . Don't worry that this is expressed as log[e(p, u)] instead of as e(p, u). After all, if we apply the exp() function to both sides, the left-hand side will become e(p, u). (a) Apply Shephard's lemma to this expenditure function to obtain the Hicksian demand for good i. (Hint: Differentiate with respect to log(pi) to obtain an elasticity that includes the Hicksian demand. Note also that p k k equals (e log(pk) ) k . The Hicksian demand should be a function of the 's, the 's, prices, and u.) (b) Derive the indirect utility function that is associated with this cost function. This is easier than part (a). (c) Finally, use your answer to (b) to obtain the Walrasian demands. What is the name of the derivation that is used to obtain the Walrasian demands?

Consider a firm that produces a single output q 0 using inputs z1 0 and z2 0, where the input-requirement set is nonempty, strictly convex, closed, and satisfies weak free disposal. Assume the firm operates in competitive markets. The firm's profit function is (r1, r2, p) = p 4(r1 + r1r2 + r2) , where p > 0 is the price of output, r1 > 0 and r2 > 0 are the input prices, and is a constant parameter. (a) What condition on (if any) is required for (r1, r2, p) to satisfy the price homogeneity property of a valid profit function? Justify your answer. (b) Use (r1, r2, p) to derive the firm's unconditional supply and factor demands. (c) Derive the firm's conditional factor demands and cost function. (d) It is easy to verify that the conditional input demands in (c) are non-increasing in their own price. Show that this result holds in general for a cost function derived from a production possibility set with N inputs and M outputs.

Consider a firm that produces output q 0 at a cost of c(q), where c 0 (q) > 0 and c 00(q) > 0. Also assume that there is a probability 1 > > 0 that the firm experiences an equipment failure and incurs additional repair costs equal to cR > 0 per unit of output or cRq in total. The competitive price of output is p > 0. (a) Derive the firm's first-order condition for an interior solution assuming its objective is to maximize expected profit. What is the economic intuition of this condition? (b) Derive the firm's first-order condition for an interior solution assuming its objective is to maximize its expected utility of profit, where the strictly increasing and strictly concave function u() characterizes its risk preferences. (c) Will the firm produce more if its objective is to maximize expected profit or if its objective is to maximize the expected utility of profit? Justify your answer and provide the economic intuition for your result.

Consider an expenditure function that has the form log[e(p, u)] = X L k=1 k log(pk) + u Y L k=1 p k k . Don't worry that this is expressed as log[e(p, u)] instead of as e(p, u). After all, if we apply the exp() function to both sides, the left-hand side will become e(p, u). (a) Apply Shephard's lemma to this expenditure function to obtain the Hicksian demand for good i. (Hint: Differentiate with respect to log(pi) to obtain an elasticity that includes the Hicksian demand. Note also that p k k equals (e log(pk) ) k . The Hicksian demand should be a function of the 's, the 's, prices, and u.) (b) Derive the indirect utility function that is associated with this cost function. This is easier than part (a). (c) Finally, use your answer to (b) to obtain the Walrasian demands. What is the name of the derivation that is used to obtain the Walrasian demands?

Consider a firm that produces a single output q 0 using inputs z1 0 and z2 0, where the input-requirement set is nonempty, strictly convex, closed, and satisfies weak free disposal. Assume the firm operates in competitive markets. The firm's profit function is (r1, r2, p) = p 4(r1 + r1r2 + r2) , where p > 0 is the price of output, r1 > 0 and r2 > 0 are the input prices, and is a constant parameter. (a) What condition on (if any) is required for (r1, r2, p) to satisfy the price homogeneity property of a valid profit function? Justify your answer. (b) Use (r1, r2, p) to derive the firm's unconditional supply and factor demands. (c) Derive the firm's conditional factor demands and cost function. (d) It is easy to verify that the conditional input demands in (c) are non-increasing in their own price. Show that this result holds in general for a cost function derived from a production possibility set with N inputs and M outputs.

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t give the answers to the following

I) Money Demand (15 points) Consider a worker with an annual income of $90,000. Suppose he receives wage payments (of equal value) three times a month. Consumption spending is constant at $90,000 a year. Assume that he holds no bonds. That is, he holds all financial assets in the form of money. Also assume that he begins the first period with no consumption goods. a. If the worker shops 6 times each month, what is the average money balance? draw a clear graph. (6 points)

b. If he shops three times a month, what will his average money balance be? Make sure that you draw a clear graph. (6 points

c. What is the relationship between the frequency of shopping trips and average money balance. (3 points)

Permanent Income (20 points) a. A consumer lives for four years. (Assume that his goal in life is to equate consumption over time) He receives $20,000 in the first year, $26,000 in the second year, $44,000 in the third year and $15,000 in the fourth year. The interest rate between the first and the second year is 4% while that between the second and the third is 3% and that between the third and the fourth is 10%. The price level is $1 in every period. What is his annual consumption? What is the amount that he saves in the third year? (12 points)

b. Suppose that the individual is diagnosed with cancer at the beginning of period 3 and knows that he will surely not survive into period 4. Assume that he is unable to borrow against his period 4 income given this health circumstance. To be clear, when he was making his consumption decisions at the beginning of period 1, he could borrow against his period 4 income, but when period 3 arrives assume that he is denied the possibility of a loan against his period 4 income. How much does he consume each year? (8 points)

III) Market Clearing (15 points) a. Suppose that the economy experiences a permanent negative shock to production. Assume that this change also shifts the marginal product of labor. Using three graphs, indicate what happens to aggregate output, Y; the interest rate R, the price level P and the real wage rate w/P. Explain intuitively what happens to the interest rate and why? Explain why the labor demand and labor supply curve move the way they did (10 points)

b. Suppose instead that the shock was temporary and did not affect the MPL. How would the labor market clearing condition be affected? Explain clearly (5 points)

you are an influential CEO of a company like Wal-Mart, who imports foreign made clothing. The government wants to restrict the quantity of the product that your company imports. Should you use your political influence to lobby the Congress to impose a tariff (import tax) on the product? (5 Marks) or should you use your political influence to lobby the Congress to impose quota (maximum amount of the import) on the product?

Blake lives in Seattle and is planning a get-away with some friends to San Diego and needs to find a hotel for her group. Blake enters "discount hotels san diego" in the Google search bar. The following screenshot shows the ads that appear in the SERP.

List the advertisers that earned an impression from Blake's search. Do you see a difference between the top listed ad and the others that earned an impression? What may have helped the top ad rank higher than the others?

Describe the concept of zero lower bound as it relates to interest rates. In the prescribed textbook, Blanchard states that the federal funds rate cannot be zero (2017: 27).

Explain why you agree or disagree with this statement.

(5)

Q.1.2

Give two equations that can be used to represent the consumption function equation.

(Hint: Name each of its components.)

(5)

Q.1.3

Distinguish between a floating (flexible) exchange rate system and a fixed exchange rate system in an open economy.