Question 6 (Cost minimization, 1 point each): The prices of inputs (x1 , X3, X4)

Question

Question 6 (Cost minimization, 1 point each): The prices of inputs (x1 , 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,x) x3 + xa, 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+ , what is the minimum cost of producing one unit of output? (d) If the production function is given by f(XyX2, X3, X4) = min(x1, X21+min(x3, X4), what is the minimum cost of producing one unit of output? (e) Which of the above production functions exhibit constant returns to scale? (Note: make sure you get the minimum cost's dollar value, not just the cost function)

Explanation / Answer

a) minimum cost is $5

b) minimum cost is $2

c) minimum cost os $3

d) minimum cost is $5

e) All four production functions defined in (a),(b),(c),(d) exhibit constant returns to scale

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