Economics problem! Help! 1.2?

Question

I was hoping someone could show me a walk-through on this problem:

The prices of inputs (x1, x2, x3, x4) are (4, 1, 3, 2).

A. If the production function is given by f(x1, x2) = min{x1,x2}, what is the minimum cost of producing one unit of output?

B. If the production function is given by f(x3, x4) = x3 + x4, what is the minimum cost of producing one unit of output?

C. If the production function is given by f(x1, x2, x3, x4) = min {x1 + x2, x3 + x4}, what is the minimum cost of producing one unit of output?

D. If the production function is given by f(x1,x2) = min {x1,x2} + min {x3,x4}, what is the minimum cost of producing one unit of output?

Answer 1

A: TC=1

You need to find combination which gives you 1 unit of output. Since factor prices are 4;1 just choose cheapest one - it will be one unit of factor x2 which cost 1

B: TC=1

Here output equals factor prices so just choose cheapest too in this case - it will be x4 price=2 and output=2 too, so divide output by price 2/2 and get cost.

C: TC=1

The same way - seek for cheapest factor one unit of x2 all the rest=0

D: TC=1

The same way - seek for cheapest factor one unit of x2 all the rest=0 - approach for solution the same.

Answer 2

The prices of inputs (x1, x2, x3, x4) are (4, 1, 3, 2).

A. If the production function is given by f(x1, x2) = min{x1,x2}, what is the minimum cost of producing one unit of output?

Ans: X2 will be used one unit . Cost will be price of X2 = 1

B. If the production function is given by f(x3, x4) = x3 + x4, what is the minimum cost of producing one unit of output?

Ans: Cost is 5

C. If the production function is given by f(x1, x2, x3, x4) = min {x1 + x2, x3 + x4}, what is the minimum cost of producing one unit of output?

Ans: Min (5, 5 )= 5

D. If the production function is given by f(x1,x2) = min {x1,x2} + min {x3,x4}, what is the minimum cost of producing one unit of output?

Ans: Cost is 5 again.

The question has not been structure properly: unless you get the input-output coefficients you cannot really solve this problem