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Midterm

ECON 6002

2019

Questions:

1. Technological Growth and Human Capital: Intuitively technological progress and hu- man capital accumulation are part of the same process. As workers acquire new skills, it becomes easier to create new ideas. Consider the endogenous growth model with human capital (H) added to the ideas production function:

A˙ = B(aLL)γ H1-γ Aθ .

Assume that L grows exogenously at the rate n (i.e. L˙ /L = n), H grows at the rate gH (i.e. H˙ /H = gH ), 0 < γ < 1, and θ < 1.

(a) If the stock of human capital H increases, what is the eﬀect on the growth rate of ideas gA = A˙ /A? (2 points)

(b) Find the steady state growth rate of ideas gA(*) . (2 points)

Hint: the quadratic formula is (-b 土^b2 - 4ac)/2a

(c) If the growth rate of human capital increases (gH 个), what is the eﬀect on gA(*)? Does this make economic sense? Explain. (2 points)

(d) According to the model, is it possible for population growth to be negative (n < 0) and for steady growth of ideas to remain positive (gA(*) > 0)? Explain. (2 points)

2. Smartphones and patience: George and Alice are arguing over the eﬀect of smartphones on kids today. George argues that smartphones make people impatient and that they are the reason that wages and interest rates are low. Alice argues that George is wrong. If smartphones make people impatient, then wages would decrease but that the interest rate would go up! Alice argues that interest rates are low because the technological growth (g) rate is low.

(a) Using the Ramsey model below, draw a phase diagram that shows the eﬀect of an increase in ρ, the time discount factor, to show how more impatience aﬀects the steady state level of intensive form capital. (2 points)

c˙ αkα -1 - ρ - θg

c θ

k˙ = kα - c - (n + g)k

(b) Using the Ramsey model above, draw a phase diagram that shows the eﬀect of an decrease in g, the growth rate of technology, to show how technology growth aﬀects the steady state level of intensive form capital. (2 points)

(d) In this model, interest rates are given by r(t) = αk(t)α -1 and wages are given by w(t) = A(t)(1 - α)k(t)α .

i. What is the growth rate of wages when k is at steady state? (2 points)

ii. What parameter (n, g , α, or θ) can cause interest rates to be low at the same time that wages grow at a slower rate on the balanced growth path? Explain. (2 points)

3. True, False, or Uncertain: Decide whether the following statements are true, false, or uncertain. Provide an explanation for your choice. Marks are awarded for your expla- nation only. Answers with correct “true” or “false” designations but incorrect explanations will receive zero marks. A few sentences or a sentence and a diagram should be suﬃcient for full marks. Each answer is worth 2 points.

(a) The Golden Rule level of capital is the amount of capital that maximizes consumption and it is never reached in the Ramsey model because households are assumed to be impatient.

(b) Comparing the predictions of the Solow-Swan model to the Ramsey model, a decrease in the population growth rate has a diﬀerent eﬀects in each model on the steady state level of intensive form capital.

(c) In the Diamond model, if there is a social security tax system that taxes the young and transfers it to the old, then the lifetime budget constraint for each individual is given by

C1,t + = Atwt - T + (1 + n)T