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ECON-UA-12

DEPARTMENT OF ECONOMICS

INTERMEDIATE MACRO

SPRING 2026

Problem Set 2

Not graded; do not turn in

Answer the following for recitations on Friday. Recitation Problem Sets help you with Quiz and Exam questions. Answers will be posted on Brightspace after recitations.

A.  Production Functions and Chapter 8

1.   Suppose the aggregate production function is Y = Ka L1- a  where 0 < a  < 1.

a.   Find the intensive form of the production function, y = f(k), where y  Y/L and k K/L

b.   Find the marginal product of labor and the marginal product of capital (MPK ∂Y/∂K). Use words to describe the MPL and MPK.

c.   Find the marginal product of capital per worker (MPk ∂y/∂k) and describe the MPk.

d.   Show that MPK = MPk.

e.    Suppose a = 1/3. If population growth is 3% and the capital stock grows 6%, use the growth trick to show that output growth is 4% and output per worker grows 1%.

2.   The aggregate production function is Y = K1/2  L1/2 . If, in the Solow model, the saving rate is 40%, depreciation is 8% per year, and the population grows 2% per year, find output per worker, capital per worker, and consumption per worker in a steady state.

B.   Problems and Applications from Chapter 8 in Mankiw

Chapter 8 Problem #1 parts b, c, d

Chapter 8 Problem #2.

Chapter 8 Problem #3 parts a and b.