Question

17. Suppose that Al Deardwarfs production function for deer lawn omaments is f(x,x)(x+2x)"2, where x, is the amount of plastic used and x, is the amount of wood used. Let w be the price per unit of plastic and w, be the price per unit of wood where w, > 2w. Then Al's supply function is: А) S(p) - р/(w; + w,) В) S(p) - p/(2w; + w;) C) S(p) p/(2w;) D) S(p) p/w E) S(p) ,p°

Please show all steps/explanations. Correct answer is C. Thanks

Answer 1

Given that w2 > 2w1 we have w1/w2 < 0.5

MRTS = MPx1/MPx2

= 0.5(x1 + 2x2)^-0.5 / 0.5*2(x1 + 2x2)^-0.5

= 0.5

Now MRTS is 0.5 and w1/w2 is less than 0.5.

Hence MRTS > w1/w2

This implies that plastic is more productive and firm uses only plastic.

This results in q = (x1 + 0)^0.5

q = x1^0.5 or x1 = q^2

Cost function is C = wL

C = w1 * q^2

Supply function is MC = P

MC = 2qw1

Hence supply function is P = 2qw1

q = P/2w1

Select option C