Brooklyn College 7025X Assignment 3 MATHEMATICAL METHODS IN ECONOMICS Spring 2015
7025X MATHEMATICAL METHODS IN ECONOMICSBrooklyn CollegeSpring 2015Project 31. Contemplate the agency with a single issue of manufacturing outlined implicitly by the relation???? = ????three + four????the place z is the variable enter and q is the output. The agency faces the next common revenuefunction:???? = 10 ? 2????Calculate the elasticity of the firm’s complete gross sales income with respect to the quantity of labor usedwhen q=2.2. The equation ????2 + ????2 + ????2 + ???????? + ???????? + ???????? + ???? + ???? + ???? ? 1 = zero has one answer (x,y,z)=(1,-1,-1). Examine that the equation does certainly outline z as a perform of x and y at this level. Calculate thepartial derivatives of z with respect to x and y at this level.Trace: Outline the equation as F(y,x,z). Take the partial derivatives of z with respect to x and y, implicitly, that's,remedy ????????????????=?????????????????and ????????????????=?????????????????. Examine if ????????????????is non zero with a view to see that the implicit perform exists. Do all thenecessary substitutions.three. Suppose you're analyzing a monopolist agency, with the next common income and common costfunctions:????????(????) = ?????three + 12????2 ? 30???? + 1000 and????????(????) = 2???? + 1000 ?100????the place s are the typical gross sales per day. If the monopolist chooses to provide nothing (s=zero), the totalcosts develop into unfavourable.i. Write an expression for the Earnings as a perform of s.ii. Decide essentially the most worthwhile stage of output. Present that this output stage does certainly leadto a most fairly than a minimal by checking the second order circumstances.four. This query will not be obligatory, however is additional credited: The next three equations outline x, yand w as capabilities of z.???????? ? ???? = zero???? = ????three + three????????three + ????three = 2????????Discover and expression for????????????????, and consider it on the level the place w=z=1. Trace: Make use of Jacobianmatrix to resolve this