a)Draw three isoquants, choosing whichever level of Q you prefer (pin down the level of Q at a

given value and then find combinations of K and L returning that specific level of Q; if the

function is non-linear, a combination of 4-5 points might be enough to give a rough idea of the

shape of the isoquant).

b) Compute the marginal product of each input and indicate whether they are decreasing, constant

or increasing.

c) Compute the marginal rate of technical substitution.

d) Indicate whether the functions exhibits decreasing, constant or increasing returns to scale.

e) Consider the following isoquants (the red L-shaped functions), drawn from a production function

where inputs (capital and labor) are said to be perfect complements; the isoquants are for Q=1

2

(the isoquant on the left), Q=3 and Q=7 (the isoquant on the right). The black line is L = K/2

.

Explain the behavior of this production function. If the firm wants to produce 3 units of output

and inputs are costly, how much inputs should it use?

3.?rnducon functions. Consider the following production functions: 1 1. Q1 = F(K, L) = KSLE 1 2.02 = F(K,L) = 2K7 + 8L 3.Q3 = F(K,L) = 4K +L where Q is the output, K is capital and L is labori For each one of them: a) Draw three isoquants, choosing whichever level of Q you prefer (pin down the level of Q at a given value and then nd combinations of K and L returning that specic level of Q; if the function is non-linear, a combination of 4-5 points might be enough to give a rough idea of the shape of the isoquant). b) Compute the marginal product of each input and indicate whether they are decreasing, constant or increasing c) Compute the marginal rate of technical substitution. d) Indicate whether the functions exhibits decreasing, constant or increasing returns to scale e) Consider the following isoquants (the red Lshaped functions), draWn from a production function where inputs (capital and labor) are said to be perfect complements; the isoquants are for Q=1 l (the isoquant on the left), Q=3 and Q=7 (the isoquant on the right). The black line is L = K 2' Explain the behavior of this production function. If the firm wants to produce 3 units of output and inputs are costly, how much inputs should it use.>