Part 1 - Question 3 · Introducció a la Macroeconomia UPF 2018

Labor market, Phillips Curve, and IS-LM-PC model

Carefully analyze the article published in The New York Times (February 2018) under the headline “The Stock Market Is Worried About Inflation. Should It Be?” and answer the questions below.

Part 1 - Question 3 (1.5 points). Solow growth model and technological progress

Consider an economy characterized by a constant savings rate $s = 0.20$ ($20\%$) and a capital depreciation rate $\delta = 0.10$ ($10\%$). The aggregate production function is:

$$Y_t = F(K_t, N_t) = K_t^{0.5} N_t^{0.5}$$

Government purchases and taxes are zero, there is no technological change initially, and the labor force $N$ remains constant.

a.

Derive the law of motion for capital per worker between year $t$ and $t + 1$. State the condition required for the steady state, write down the corresponding equilibrium equation, and compute the steady-state values of capital per worker ($K^*/N$), output per worker ($Y^*/N$), and consumption per worker ($C^*/N$).

b.

Suppose the economy has attained its steady state. In year 2020, a technological breakthrough permanently updates the aggregate production function to:

$$Y_t = F(K_t, N_t) = 2 K_t^{0.5} N_t^{0.5}$$

Compute capital per worker, output per worker, investment per worker, and consumption per worker in year 2021.

c.

Determine the new steady-state values of capital, output, and consumption per worker under this enhanced technology. Describe the graphical representation of this adjustment process and explain how the transition unfolds starting from the 2021 dynamic values computed in 3.2.