# Essay about Homework 2 solution

Department of Economics

Econ 4331w: Economic Development

Homework Assignment 2 - Answer Key

Exercise 1

a) (5 points) Describe the …nal goods producing sector in the Romer model. Is there perfect or imperfect competition? Write down the problem of the …rm in this sector and derive the …rst order conditions for optimality. Answer: This sector produces the …nal good using intermediate goods and sells that good to consumers. There

RA

are a large number of perfectly competitive …rms using the CRS production function Y = L1 xj dj. The

Y

0

…rm’ problem is s Z A

Z A

1

pj xj , max LY xj dj wLY

LY ;xj

0

0

and the …rst order conditions are

[LY ]

[xj ]

: (1

:

) LY

L1

Y

A

xj dj

*…show more content…*

P1

pro…ts; Hint 2: if a 2 (0; 1), then t=0 at = 1= (1 a)). Answer this question for the following possibilities:

a) (5 points) The monopoly pro…ts are constant. That is,

t

=

for all t.

Answer: The price of the patent, PA , will be equal to the present value of future pro…ts, that is

PA =

1

X

t=1

t t (1 + r)

where the summation starts at t = 1 because that is when whoever buys the patent will start to receive the pro…ts. Notice that since t = for all t,

PA =

1

X

t=1

1

1+r

t

,

and that since r > 0, it follows that 1= (1 + r) < 1 and we can solve this using the simple geometric series formula !

!

1 t X

1

1

1+r

PA =

1 =

1 =

1

1

1+r

r

1 1+r t=0 and …nally, we get

PA =

3

r

:

b) (5 points) The monopoly pro…ts are grow at a constant rate n. That is, and suppose that n < r.

1 =

t+1

= (1 + n)

t

for all t. Let

Answer: Here we can follow the same procedure. Again

1

X

PA =

t=1

Since

t+1

= (1 + n)

t

for all t with

1

=

t

t:

(1 + r)

it follows that t 1

t

hence,

PA =

1

X (1 + n)t t=1 = (1