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School of Economics

ECON6002

Practice Mid-Semester Test


Examinable Material and Expectations:

1. The mid-semester test will cover material from Weeks 1-5, corresponding to Romer, Chapters 1-5. Anything covered in the lectures, in the tutorials, or in the first problem set is examinable.

2. I will provide relevant formulas such as production functions to be used in answering a question (see questions below to see examples of what sort of material will be provided and what you might be assumed to know).

3. You will be expected to understand the “economics” behind any equations provided.

4. In answering questions, be precise, showing all of the steps, and indicate if you are making any assumptions along the way.


Practice Mid-semester Test Questions:

1. Consider the Solow-Swan model in continuous time with the Cobb-Douglas aggregate pro-duction function,  Steady-state consumption per unit of effective labour is Assume = 0.5, population growth = 5%, technology growth = 10%, and depreciation rate = 10%.

(a) In addition to the Inada conditions, what is the condition in terms of the sum of , and for a unique steady state with positive to exist? What is the numerical value of + + for this economy? (1 point)

(b) Solve for the “Golden Rule” saving rate and capital per unit of effective labour, , that maximize steady-state consumption per unit of effective labour. (2 points)

(c) Assume the economy is on its balanced growth path and the current saving rate is  = 60%. Compute steady-state capital per unit of effective labour and the growth rate of aggregate capital  along the balanced growth path. (2 points)

(d) Is the economy saving too much or too little along its balanced growth path? Why? (2 points)


2. Consider the Ramsey model in continuous time with a Cobb-Douglas aggregate production function,  The Euler equation that describes the optimal growth path of consumption per person is

where Capital per unit of effective labour evolves according to  Suppose the economy is initially on the balanced growth path.

(a) Why does the particular growth rate of consumption depend on (recall 1/ is the intertemporal rate of substitution)? (3 points)

(b) Derive the steady-state values of and as functions of the model parameters. (2 points)

(c) Suppose that at time t0, households suddenly become less patient (i.e. increases). Assume that this change in household patience is permanent. Explain both the short-run and long-run dynamics of c(t) and k(t) and draw the transition path for the economy using a phase diagram. (3 points)


3. In the simple endogenous growth model, the output production function is and the production function of new ideas is  where population grows at rate n.

(a) The parameter captures the marginal impact of the stock of knowledge on the growth of new ideas. If > 0, how would the stock of knowledge affect the growth of new ideas? How about < 0? (2 points)

(b) Solve for the growth rate of , i.e. , in terms of model parameters and . What is the steady-state growth rate of ideas if < 1 and > 0? (2 points)

In the Romer model, the first-order conditions for the profit-maximizing firms imply (amongst other things) that and . Also, the equilibrium output growth is max .

(c) 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)

(d) Given determines the substitutability among labour inputs in the Ethier production function, with higher corresponding to more substitutability, what is the economic interpretation of the exponent  in the expression for L(i) 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? (2 points)


4. In the special case of the RBC model, the equilibrium saving rate is , < , and labour supply per person is , where α is the capital share in the Cobb-Douglas production function, , n is the population growth rate, is the discount rate, and b is the weight on (log) leisure in the instantaneous utility function.

(a) What simplifying assumptions are necessary in this special case of the model to have a unique equilibrium with a constant saving rate? (2 points)

(b) Show that equilibrium labour supply, , would decrease if the capital share increased (i.e., ↑). Explain why. (2 points)

(c) Describe in words how the equilibrium can be solved for in this case of the RBC model. (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?) (3 points)