Question: man q1...its complete help megg

(Production functions, inputs are perfect complements) Fine epoxy is used to produce LEDs and other electrical components. To get stable, good qualities (durability, resistance, adhesion) epoxy, the epoxy resins (R) are cured ("linked") to hardeners (H) like amines and acids, at the following fixed proportion: to produce 1 unit of final epoxy, we need to cure 2 units of R with 1 unit of H. Let be the quantity of final epoxy produced, (, ).

Then, the production function of epoxy is given by: (, ) = 1 2 min(, ), for some positive numbers and .

a. What is and ?

b. If we want to produce 10 units of the final product epoxy, what would be the least amount needed of R and H?

c. Does the production function of epoxy exhibit increasing, constant, or decreasing returns to scale? (IRS, CRS, or DRS?)

d. Draw a map of some isoquants of this production function

We will go through the derivation of the model, and along the way compare/contrast it to similar models seen in lectures 2-4. 1. Interpret the constraint in equation (5) of the paper. How does this compare to the constraint in Gine and Townsend (2004). What values correspond to the two sectors of that economy. 2. How is talent modeled in this paper. Derive the cuto talent point z. In Buera, Kaboski and Shin (2010) cuto talent depends on asset. Is it the case here? Name two factors behind the dierence. 3. What occupation choice, if any, does individuals face in this paper? How does this aects market clearing compared to the models we have seen in class? 4. From the rms problem, you should nd that prot is linear in asset. Show and explain how this translate to a linear saving policy. 5. Solve for the market equilbrium, and show that the economy on aggregate is equilavent to a Solow model. Write down the expression for TFP. How does it depend on talent of individuals in the economy. 6. Given stationary wealth shares !(z), show that in the steady state K = Y + 7. Your friend just read Japelli & Pogano (1994), which found that country with tighter credit constraint has higher K : Y He sees equation in #6, and conclude that in this paper, credit constraint does not aect the economy. How would you explain to him. 8. The paper denes !(z; t) as the share of wealth held by talent type z at time t: Describe lim !(z; t) for t!1 the case where (i) individuals talent is xed; and (ii) individuals talent is i.i.d. over time. Which case leads to higher GDP in the long run? How about in the short run?

We will go through the derivation of the model, and along the way compare/contrast it to similar models seen in lectures 2-4. 1. Interpret the constraint in equation (5) of the paper. How does this compare to the constraint in Gine and Townsend (2004). What values correspond to the two sectors of that economy. 2. How is talent modeled in this paper. Derive the cuto talent point z. In Buera, Kaboski and Shin (2010) cuto talent depends on asset. Is it the case here? Name two factors behind the dierence. 3. What occupation choice, if any, does individuals face in this paper? How does this aects market clearing compared to the models we have seen in class? 4. From the rms problem, you should nd that prot is linear in asset. Show and explain how this translate to a linear saving policy. 5. Solve for the market equilbrium, and show that the economy on aggregate is equilavent to a Solow model. Write down the expression for TFP. How does it depend on talent of individuals in the economy. 6. Given stationary wealth shares !(z), show that in the steady state K = Y + 7. Your friend just read Japelli & Pogano (1994), which found that country with tighter credit constraint has higher K : Y He sees equation in #6, and conclude that in this paper, credit constraint does not aect the economy. How would you explain to him. 8. The paper denes !(z; t) as the share of wealth held by talent type z at time t: Describe lim !(z; t) for t!1 the case where (i) individuals talent is xed; and (ii) individuals talent is i.i.d. over time. Which case leads to higher GDP in the long run? How about in the short run?

(a) Given the production function given in formula (3) of the paper, solve the cost minimization problem Ms PsYs = minPsiYsi i=1 subject to 1 Ms 1 Y s = Ysi . (2) i=1 Determine Ps. (b) Let s be the multiplier on the constraint (2). Show that the profit maximization of firm i in industry s is 1 max (1 1 Ysi ) s (Ysi) wLsi (1 + Ksi) RKsi Y si,Lsi,Ksi subject to Y = A Ks 1 si si si L s si . (c) Use the solution to the firm maximization problem and the expression of Ps to derive the formula (15). NOTE: In their original QJE paper, there are a couple of typos! In particular, (12) and (13) are not correct if MRPLs and MRPKs are defined as in their paper following (12) and (13). As a hint: define s = s M 1 1 PsiYsi MRPL MRPLsi PsYs i=1 and MRPKs similarly. (d) There is a large literature trying to link the distortions (Ysi , Ksi ) to financial frictions individual firms face. To see the relation between these exogenous taxes and credit constraints, suppose that there are no taxes (i.e. Ysi = Ksi = 0) but firm i faces a credit constraint of the form wLsi + RKsi W (zsi, ), where zsi is a firm characteristic (e.g. wealth), parametrizes the financial system and parametrizes how much of capital expenses can be pledged. Suppose that W is increasing in both argument, i.e. wealthy firms are less constrained and better financial system are associated with higher values of . Derive the firm's factor demands taking prices factor prices as given. What are the firm-specific "taxes" in this framework? Suppose that Asi = A, i.e. all firms have the same productivity. Which firms face high "output-taxes Ysi "? Under what conditions would a researcher conclude that Ksi = 0?

[Part II] This part concerns the analysis of equations in Appendix I in the paper. (a) Show that TFP = TFPR w TFPR = M Li P TFPRi in which i=1 L (b) Suppose (1 i) = a 1 Ai . Using the labor market clearing condition, show that 1 TFP = M M i=1 Ai L1 independent of a. Give a concise interpretation why aggregate TFP is independent of a. What is the crucial assumption for this result?

We will go through the derivation of the model, and along the way compare/contrast it to similar models seen in lectures 2-4. 1. Interpret the constraint in equation (5) of the paper. How does this compare to the constraint in Gine and Townsend (2004). What values correspond to the two sectors of that economy. 2. How is talent modeled in this paper. Derive the cuto talent point z. In Buera, Kaboski and Shin (2010) cuto talent depends on asset. Is it the case here? Name two factors behind the dierence. 3. What occupation choice, if any, does individuals face in this paper? How does this aects market clearing compared to the models we have seen in class? 4. From the rms problem, you should nd that prot is linear in asset. Show and explain how this translate to a linear saving policy. 5. Solve for the market equilbrium, and show that the economy on aggregate is equilavent to a Solow model. Write down the expression for TFP. How does it depend on talent of individuals in the economy. 6. Given stationary wealth shares !(z), show that in the steady state K = Y + 7. Your friend just read Japelli & Pogano (1994), which found that country with tighter credit constraint has higher K : Y He sees equation in #6, and conclude that in this paper, credit constraint does not aect the economy. How would you explain to him. 8. The paper denes !(z; t) as the share of wealth held by talent type z at time t: Describe lim !(z; t) for t!1 the case where (i) individuals talent is xed; and (ii) individuals talent is i.i.d. over time. Which case leads to higher GDP in the long run? How about in the short run?

Consider a horizontally differentiated product market in which two firms are located at any points l1 and l2 on the real line, respectively, with the notation l1 l2. Firms produce at marginal costs c. There is a continuum of consumers of mass 1 who are uniformly distributed on the unit interval. They have unit demand and have an outside utility of . A consumer located at x [0; 1] obtains indirect utility v = max (v1; v2) with v1 = r (x l1) 2 p1 if she buys one unit from firm 1 and v2 = r (l2 x) 2 p2 if she buys from firm 2. Firms have marginal costs equal to c.

a. Suppose that prices are regulated at pi = 2c. In the game in which firms simultaneously decide where to locate their product, characterize the Nash equilibrium.