1) Consider the Production functions. Indicate whether these functions are decreasing

returns to scale, constant returns to scale or increasing returns to scale.

a) 2K + L

b) K²/L³

c) K^0.3L^0.7

 

2) What are some factors that cause an increase in investment in a small closed economy?

How does this affect trade surplus/deficit? Explain in words and show graphically.

1.

a.

Constant Returns to Scale

b.

Decreasing Returns to Scale

c.

Constant Returns to scale.

2.

Explained in explanation part.

1.

a.

Production function:

F(K,L) = 2K + L

F(aK,aL) = 2aK + aL

= a(2K + L)

=a F(K,L)

Here, the power of 'a' is one, thus, this production function shows the constant returns to scale.

b.

F(K,L) = K²/L³

F(aK,aL) = (aK)₂/(aL)₃

= 1/a * K²/L³

= a^(-1) K²/L³

_­­The power of 'a' is less than 1 thus; it shows the decreasing returns to scale.

c.

F(K,L) = K^0.3L^0.7

F(aK,aL) = (aK)^0.3  (aL)^0.7

 ₌ a K^0.3L^0.7

The power of 'a' is equal to 1 thus; it shows the constant returns to scale.

2.

The investment shows the negative relationship between interest rate. It is because as the interest rate decreases then the investment becomes more profitable for the firms in the market thus, they increase the investment as interest rate decreases and vice-versa. Graphically, it can be indicated as follows:

There are many other factors which affect the investment in the economy which are economic growth, business confidence, state of technology, availability of finance etc. The changes in these factors causes to shift in the investment demand curve. 

please see the attached file for the complete solution.