Please help me in showing how m_v and m_s can be a ratio as part (a) asks for

Problem 1: \"Prices\" of Inputs and the Elasticity of Substitution in the Matching Technology (30 points). The goods-production technology f (k,,n,) takes as inputs the two arguments k, and n, . It is widely accepted in the profession that the prices for the inputs k, and n, are, respectively, the real interest rate 7'1 and the real wage wt. By analogy, a recent idea that has emerged is that, at least in principle, the \"inputs\" 5, and v, in the matching technology m(s,,v,) also have \"prices\" attached to them. Denote the input price for s, as p3, and for v, as p,, . For the ensuing analysis, take as given that these prices p3, and pv, do exist and (importantly) can be measured. The matching technology is of the following functional form _S_t v1 m(s,,v,) =v,- 16 For this matching technology, the marginal product (i.e., the rst partial derivative) with respect to v, is HINT: For use below, the first derivatives of the exponential function are derivative of es,/v. = es, /v. w.r.t. est/v, derivative of es/v, = es,/v. w.r.t. s, derivative of es,/v, = -es, /v. S w.r.t. v.a. (3 points) Based on the given marginal products ms and m for the matching technology stated above, display the ratio m" as m5 my _ m S in which the term in ellipses is left for you to determine. Clearly display any algebraic steps