midterm

Practice Problem for Midterm 2 Econ 100B, Winter 2021

1. State whether the following production functions exhibit increasing, constant, or decreasing

returns to scale in K and L.

(a) Y = K1/3L1/2

(b) Y = K2/3L

(c) Y = K1/2L1/2

2. Write down the firm’s profit maximizing problem. Be sure to identify the variables the firm

can choose and which it takes as given. What should the firm facing the following scenarios

do?

ˆ If the marginal product of capital is greater than the rental price of capital.

ˆ If the marginal product of labor is less than the wage.

3. Show the transition dynamics in the Solow model if s̄Yt < d̄Kt.

4. Given a production function Yt = ĀK 1/3 t L̄

2/3, if Ā = 2, L̄ = 4, s̄ = 0.2, and d̄ = 0.05.

(a) Calculate the steady-state level of capital.

(b) Does the above production function exhibit constant returns to scale? Or does it exhibit

diminishing marginal returns? Explain, including defining the difference between these

two concepts.

5. Consider the following Romer model of economic growth:

Yt = AtLyt

∆At+1 = z̄AtLat

Lat + Lyt = L̄

Lat = l̄L̄

(a) If A0 = 100, l̄ = 0.1, z̄ = 1/3000 and L̄ = 1000, what is the growth rate of knowledge

in this economy?

(b) What is the growth rate of per capita output in this economy?

(c) Using the information from year 1, what is the level of per capita output in this economy

in year 5?

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