Question

1. Determine whether each of these production functions has constant, decreasing, or increasing returns to scale:

(a) F(K,L)= K^2/L
(b) F(K,L)=K+L

2. Which of these production functions have diminishing marginal returns to labor?

a) F(K,L)=2K+15L

b) F(K,L)=√KL

c) F(K,L)=2√K+15√L

3. For any variable X, ΔX = “change in X ”, Δ is the Greek (uppercase) letter delta, Examples: If ΔL = 1 and ΔK = 0, then ΔY = MPL.

More generally, if ΔK = 0, then Δ(Y − T ) = ΔY − ΔT , so ΔC = MPC × (ΔY − ΔT ) = MPC ΔY − MPC ΔT

Now Suppose MPC = 0.8 and MPL = 20. For each of the following, compute ΔS:

a.ΔG = 100

b.ΔT = 100

c.ΔY = 100

d.ΔL = 10

4. Suppose the tax laws are altered to provide more incentives for private saving. (Assume that total tax revenue T does not change.) What happens to the interest rate and investment?

Answer 1

1. To figure of the given production functions exhibit CRS, IRS or DRS we must raise input by a constant and check the impact on output level. If on raising both input by a constant C raises output by exactly C then production function exhibits CRS. If on raising both inputs by C, output rises by more than C then IRS and if output rises by less than C then DRS.

(A) F(K,L) = Q = K^2/L

Raising inputs by c, we have-

(cK)^2/cL = c^2/c × K^2/L = c. Q.

Here when we raised both K and L by c, output Q also rose by c. So production function exhibits CRS

(B) F(K,L) = Q = K+L

Let's raise by c both the inputs, we have -

aK + aL = a(K+L) = aQ.

Here also on raising inputs by c the output also rises by c. So production function exhibits CRS.