$$

Suppose a firm' s production function is $f(x_1$;$x_2)=x_1^{\frac{1}{4}}{x}_2^{\frac{1}{4}},$ the price for output is p ; and the prices

for the inputs are $w_1=1$ and $w_2=2.$ The long run supply function and the firm' s cost function are

and $-.$

$\frac{p}{2\sqrt[\phantom{2}]{2}}$;$2\sqrt[\phantom{2}]{2}{y}^2$

$\frac{p}{4\sqrt[\phantom{2}]{2}}$;$4\sqrt[\phantom{2}]{2}{y}^2$

$\frac{p}{4\sqrt[\phantom{2}]{2}}$;$2\sqrt[\phantom{2}]{2}{y}^2$

$\frac{p}{2\sqrt[\phantom{2}]{2}}$;$4\sqrt[\phantom{2}]{2}{y}^2$

$<mtext></mtext><mi></mi><mi></mi><mi></mi>$