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You have that in equilibrium each factor is paid its marginal product, so $$\tag1\frac{w_i}{p_i}=B_if'(l_i)$$ and $$\tag2\frac{r_i}{p_i}=f(l_i)-K_if'(l_i)\frac{B_iL_i}{K_i^2}=f(l_i)-l_if'(l_i)$$ so deviding (2) by (1) we have: $$\tag3\frac{r_i}{w_i}=\frac{f(l_i)-l_if'(l_i)}{B_if'(l_i)}.$$ Take the derivative of $r_i/w_i$ with respect to $l_i$: $$\tag4\...


1

four things : The desired result is actually which is the answer you are getting if you multiply the negative into the denominator( you can cross-check on https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution) . However, you have made the following mistakes. NON CONSEQUENTIAL ERROR: Your first error is when you differentiate to get MP1 and MP2....


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