闪电代写 -代写CS作业_CS代写_Finance代写_Economic代写_Statistics代写_代码代做_IT代写_加急帮助

Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Practice Mid-Semester Exam

ECON 6002

Semester 1, 2022

Practice Mid-semester Exam Questions:

1. In the Solow-Swan model, steady-state consumption is c* = f (k* ) _ (n + g + δ)k* . Let n = 0.05, g = 0.1, and δ = 0.1.

(a) In addition to the Inada conditions, what is the condition in terms of the sum of n, g , and δ for a unique steady state with positive k* to exist? What is the numerical value of n + g + δ for this economy? (2 points)

(b) Solve for the “Golden Rule” capital per unit of eﬀective labour, kG(*)R , that maximizes consumption if f (k) = ka , α = 0.5, n = 0.05, g = 0.1, and δ = 0.1. (3 points)

2. In the Ramsey model, the Euler equation describes the optimal growth path of consumption per person as = .

(a) Explain in economic terms why r(t) > ρ leads to > 0? (2 points)

(b) Why does the particular growth rate of consumption depend on θ (recall 1/θ is the intertemporal rate of substitution)? (2 points)

(c) Why does consumption immediately jump up if households suddenly become less patient (i.e., ρ t)? Draw the phase diagram and transition path of the economy to the new steady state. (4 points)

3. In the Romer model, the ﬁrst-order conditions for the proﬁt-maximizing ﬁrms imply (amongst

士

other things) that L(i) = ┌ ┐ 士 − φ and p(i) =w t）. Also, the equilibrium output (per capita) growth is max , B _ (1 _ φ)ρ, 0← .

(a) In words, provide an economic interpretation for the decision by output good ﬁrms about how much labour to employ in producing output (i.e., L(i)). (2 points)

(b) Given φ determines the substitutability among labour inputs in the Ethier production

function, with higher φ corresponding to more substitutability, what is the economic

士

interpretation of the exponent o in the expression L(i) = ┌ ┐ 士 − φ and what does it

imply about the price, p(i), an R&D ﬁrm can charge for use of its labour services L(i) relative to its marginal costs? (3 points)

(c) Why is there no endogenous growth if the discount rate ρ > B ? (Hint: What does the discount rate ρ imply about present value discounting?) (2 points)

4. In the RBC model with 100% depreciation and no government, the equilibrium saving rate is sˆ = αen-o , n < ρ, and labour supply per person is /ˆ = , where α is the capital share in the Cobb-Douglas production function, y = ka , n is the population growth rate, ρ is the discount rate, and b is the weight on (log) leisure in the instantaneous utility function.

(a) Show that equilibrium labour supply, /ˆ, would decrease if the capital share increased (i.e., α t). Explain why. (3 points)

(b) Describe in words how the equilibrium can be solved for in this case of the RBC model. (Hints: Decentralized equilibrium or social planner? What choice variables do you need to solve for that determine the remaining variables? What equilibrium conditions do you need to solve for these variables? What do you do to the equilibrium conditions and what do you substitute in for when solving? Do you need to posit a solution for any variables in order to solve?) (4 points)

5. Consider the role of diﬀerent frictions in explaining why monetary policy shocks have real eﬀects.

(a) In the imperfect competition/menu cost model of nominal rigidity, the ﬂex-price equi- librium relative price is Pi/P = Yy -1 , where η > 1 is the elasticity of elasticity of demand for good i and 1/(γ _ 1) is the elasticity of labour supply with γ > 1. Noting that Yi = Y and Pi = P in equilibrium, derive an expression for yi in terms of pi _ E[p], γ, and η . (2 points)

(b) Discuss why it is necessary to have both a nominal friction and a real rigidity for the nominal rigidity to explain why aggregate demand shocks can have sizeable eﬀects of real GDP in the imperfect competition/menu cost model of nominal rigidity. (2 points)

(c) In the Lucas islands model, the Lucas supply curve is y = g之(2)‰(2) (p _ E[p]), where σ之(2) > 0 is the variance of the good-speciﬁc taste shock and σm(2) > 0 is the variance of the aggregate demand shock. Noting again that Yi = Y and Pi = P in equilibrium, use the Lucas supply curve to derive a comparable expression for yi in terms of pi _ E[p], γ, and the signal-to-noise ratio λ 三 g之(2)‰(2) . (2 points)

(d) Discuss why the Lucas model suggests aggregate demand cannot have lasting eﬀects on real GDP. Why is this an example of the Lucas critique? (2 points)