Question

In Problem 12, Al’s production function for deer is f(x₁, x₂) = (2x₁ + x₂)^1/2, where x₁ is the amount of plastic and x₂ is the amount of wood used. If the cost of plastic is $8 per unit and the cost of wood is $1 per unit, then the cost of producing 7 deer is

	a.	$49.
	b.	$28.
	c.	$196.
	d.	$7.
	e.	$119.

step by step, please

Answer 1

Option (a).

Q = f(x1, x2) = (2x1 + x2)^1/2

(2x1 + x2)^1/2 = 7

Squaring both sides,

2x1 + x2 = 49

Total cost (TC) = w1.x1 + w2.x2

TC ($) = 8x1 + x2

For a linear production function, the inputs are substitutes and isoquant is a straight line touching both axes. Optimal input combination lies at one of the corner points (i.e. either x1 or x2 will be used).

From production function,

When x1 = 0, x2 = 49 and TC ($) = 8 x 0 + 49 = 49

When x2 = 0, x1 = 49/2 = 24.5 and TC ($) = 8 x 24.5 + 0 = 196

Since TC is lower when x1 = 0 and x2 = 49, this is optimal input combination with total cost of $49.