1. Solow review Recall that in equilibrium, the "birth and death of capital lines" cross so that: (nd)k=sy = ska a) Use some algebra to solve for equilibrium value of k. b) Compare this to r-code for k[t] in the loop of the function. What if any differences to do you see? c) Let a = .3, d = .1, and s = .25. What will be the ratio of steady state capital per person with a population growth rate of 0.25% to that of a population with growth rate 0.5%? (These is roughly in line with the difference between the two scenarios for 2010 to 2060.) Is this much of a difference? (1 sentence is fine.)
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- An economist fits the following production function to data from Australia and New Zealand, Y = AK" L1-« She estimate that for Australia, a = = 0.7. She estimates that for New Zealand, a = = 0.2 Based on this information, which of the following statements is most likely to be correct. There is not enough information to comment on the relative capital intensities Production wilI be relatively more capital intensive in New Zealand than in Australia Production will be relatively more capital intensive in Australia than in New Zealand Production will be equally as capital intensive in each country since they both experience constant returns to scaleYour landlord lets you grow plants in the yard, but limits the amount of water you may give them to 24 gallons a month. You may plant cacti and/or palms. Each month, a palm tree requires 8 gallons of water; a cactus needs 2. Put QP, the number of palms grown, on the vertical axis, and use QC for how many cacti you grow. Assume that it is possible to grow fractional quantities of both types of plant, for example, % of a palm tree. Show Transcribed Text 4. What is the opportunity cost of maintaining a cactus (measured in palm trees forgone)? A. 1 C. D. B. E. F. G. H. SABCDEFGH 4 1/4 1/3 D. 24 3 1 B. 4 5. What is the opportunity cost of maintaining a palm tree (in cacti forgone)? A. Cannot be known from the information provided None of the above (Explain why: C. 1/4 1/3 S C E. 24 F. 3 G. Cannot be known from the information provided H. None of the above (Explain why: Outside it On it At one of its endpoints 6. Where is the combined output of 2 palms and 3 cacti in relation to the PPF? A.…How does it go from qi = (1 - q1 - q2 - ... - qn - c)/2 to q = (1 - cq)/(n + 1) via the substitution in the last step?
- how to construct: can you explain all parts max┬(v^'∈[0,1]) Pr(b_2<b(v^' ))(v_1-1/2 (b(v^' )+E[b(v_2 )∣v_2<v^' ]))". "1. Write this system of equations in matrix form. X1 + X2 + X3 = 1; x1 – X2 = 4; X2 + X3 = 7.1. Consider the following system of equations. Y₁, Y₂ and Y3 are endogenous variables and X₁, X₂ and X3 are exogenous variables. Y₁ = a₁ + a₂Y₂ + α3Y3 + α4X₁ + α5X₂ + U₁ Y₂ B₁ + B₂Y₁+B3Y3+ B4X2+U2 Y3 = V₁ + V2X1 + Y3X2 +Y4X3 + Uz (Eq. 1) (Eq.2) (Eq.3) a) Determine if each equation is just identified, over identified or unidentified. Consider both rank and order conditions. the outem is
- Suppose in our model, lifespans increased due to a productivity in- crease. What would likely happen to hours worked and leisure over the lifetime of a representative consumer. (a) Let’s consider one of two common ways of implementing this change. Suppose the increase raised both lifespans and the amount of years consumers are healthy enough to work by the same amount, how would that likely affect the measured numbered of hours work by prime aged adults within a given year? What would likely hap- pen to the retirement age? (b) Let’s consider the other way to implement it. Suppose the change in lifetimes came about changes in technology that delayed death but did not extend the amount of years consumers are healthy enough to work. What would likely happen to hours worked within a year? What would happen to the retirement age? (c) In the US, the generalized stylized fact is that the actual age of retirement is not increasing. Nor are hours worked per week. Why are both of the…An example of the interaction term between two independent, continuous variables is: a. Yi = B0 + B1Xi+ B2DI + B3(Xi× Di) + ui. b. Yi = BO + B1X1¡+ B2X21+ ui. c. Yi = B0 + B1D1¡+ B2D2I+ B3 (D1i× D2i) + ui. d. Yi = B0 + B1X1¡ + B2X21+ B3(X1i× D21) + ui. e.All of the above. f. None of the above.Anation with fixed quantities of resources is able to produce any of the following combinations of carpet and carpet looms: Yards of Carpet (Millions) Carpet Looms (Thousands) 75 60 20 45 35 30 45 15 50 50 These figures assume that a certain number of previously produced looms are available in the current period for producing carpet. To answer this question, assume carpet looms is on the y-axis and yards of carpet is on the x-ais The plot of these points that make up the PPF has a vertical intercept of and a horizontal intercept of This PPF would be (Enter your responses as a wvhole number) bowed out a straight line
- 8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C₂) = (C₁) ¹ (C₂) ¹. We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual (b) Solve for the optimal allocation of (c, c) for all future generations. What the optimal k* ? Now suppose an…8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C₂) = (C₁) (c₂) } . We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual (b) Solve for the optimal allocation of (c₁, c₂) for all future generations. What is the optimal k* ? Now suppose an…Consider the path of output per person over time in the Romer model shown below, where the y-axis is the natural log of output per person (which is equivalent to using a ratio scale on the vertical axis). population Output per Person ideas efficiency parameter 3.5 3 2.5 0.5 O share of labor engaged in production saving rate O growth rate of the population 0 0 2 ——————- 4 Time At time t = 3, the change in the trajectory of this economy can be explained by a change in one of the parameters of the Romer model, namely an increase in 6 8 10 Pa