Consider a rm with the following production function:

f(x1; x2) = 2x1 + x2;

where x1 and x2 are the amounts of input 1 and input 2, respectively. Let the amount of

output be denoted by y while the prices of input 1 and input 2 be denoted by w1 and w2,

respectively. Assume the rm is able to choose the amount of either input (i.e., it is in the

long-run circumstance).

a) State the rm's cost minimization problem.

b) Derive the equations for isoquants and isocost curves. Show them on a diagram.

c) Derive the rm's conditional input demands.

d) Derive the rm's total cost function.

Suppose now that the rm is in a short-run circumstance. In particular, the amount of input

2 that can be used for production is xed at K > 0, i.e., x2 = K.

e) Derive the rm's short-run total cost function.

f) Show the rm's long-run and short-run total cost functions on the same diagram (put

the amount of output produced, y, on the horizontal axis).