plese use handritte solution and write code at the end "wert23"

What can explain the income disparity around the world? The differences in capital and/or labour stock? This is one of the major challenges we face today. In the context of Solow growth model, we can translate this question as follows: would a higher population growth rate be enough for a low-income country to catch up with rich countries? Or more specifically, what's the elasticity of y at y" with respect to n? Follow the steps below to find it a. Elasticity is (n/y )(dy*/dn). Use y* = f(k ) to find dy*/dn b. In the answer above you have dk'/dn. To find it use the breakeven condition, and take the derivative of both sides of this expression. c. Substitute it to what you have in (a) d. To get rid of s (saving rate) in the resulting expression, use again the breakeven condition and substitute it to what you have found in (c). e. Now you have dy"/dn. Find the elasticity as defined in (a). f. Finally simplify it by using ag = f (k )k'/f(k" ) Now, use what you found in (f) to answer the following question: If ax= 1/3, g = 2%, by about how much does a fall in n from 2 percent to 1 percent raise y"? Can population differences explain the income disparity around the world?Consider the following constrained optimization problem: T-1 MAX S.t. With = (1 +r)(m -c), t= 0.1.2, ... .T- 1 where a is consumption in period f and w, the remaining wealth at the beginning of period f. wy is the given initial wealth. (1) Assigning the current value multipliers to the constraints, derive the Lagrangian equation for the problem. (10 pts.) (2) Derive the necessary and sufficient conditions for optimality. (10 pts.) (3) From the conditions in (2), derive the Euler equation for the consumption. (10 pts.) Let's consider the same optimization problem in the question 1. (1) Derive the value function for time period . (10 pts.) (2) From the value function in (1), derive Bellman's equation for this problem. (10 pts.) (3) Derive the first-order condition of the Bellman's equation in (2). (10 pts.) (4) Derive v.(wy+1). (Hint: find Bellman's equation for s,+ 1(w,+1) and then apply the Envelope theorem to get in (+1)). (20 pis.) (5) Derive the first-order condition for 1 (wt+). (10 pts.) (6) By combining the results in (3), (4) and (5), derive the Euler equation for the consumption. (10 pts.)Principles of Microeconomics Spring 2020-Exam No. 2 FORM A Part A. Answer all of the questions (3 points each). Use the table below to answer the next 5 questions. Assume the firm operates in a pure competition market. TC TC 25 35 70 44 84 51 105 What is the average variable cost of producing 5 units? a. $9 b. $10 C $14 d. $70 2. What is the marginal cost of producing the third unit? n. $7 b. 58.67 d. $51 3. What is the average total cost of producing 4 units? a. $8.75 b. 59 c. $10 d. $15 4. If output sells for $9 per unit then how many units should the profit-maximizing firm produce? a. 0 b. 4 C. 5 d. 6 5. If the price is now $8 then how many units should the firm produce? b. 3 C. 4 d. 5 Which of the following forms of business organization is most numerous in the United States? a. partnerships C. corporations b. proprietorships d. government-owned firms