1. Consider the production function y = min {x₁, x₂}
a. Is this production function strictly concave?

b. Does this production function display increasing, constant or decreasing returns to scale?

c. Find the corresponding minimum cost function assuming that w₁ and w₂ are given.

2. Consider the production function y = x₁ + x₂.
a. Is this production function strictly concave?

b. Does this production function display increasing, constant or decreasing returns to scale?

c. Find the corresponding minimum cost function assuming that w₁ and w₂ are given.

3. Consider the following production function: f(x)= x₁^1/3 x₂^1/3

a. Find the marginal productivity functions. Are they decreasing?

b. Does this production function display increasing, constant or decreasing returns to scale?

c. Assume that p₁, w₁ and w₂ are given. Write pro?ts as a function of the level of inputs and ?nd the optimal amount of input x*₁ and x*₂. How do the demands of inputs depend on p, w1 and w2?

d. Using the previous solution ?nd the supply function. How does y* depend on p, w1 and w2?

e. Find the minimum cost function. How does it depend on w1, w2 and y?

f. Graph the minimum cost and marginal cost functions (assume w1 = w2 =1).

g. Find the optimal amount of output y*. How does it compare with the solution in point d?

h. Using the previous solution ?nd the input demand functions. How does it compare with the solution in point c?