Let the equilibrium condition for national income be ?(?) + ?(?) = ?(?) + ? (? ′ , ? ′ ,? ′ > 0; ? ′ + ? ′ > ? ′ ) Where S, Y, T, I and G stand for saving, national income, taxes, investment and government expenditure respectively. All derivatives are continuous a. Interpret the economic meaning of the derivatives ? ′ , ? ′&? ′ b. Check whether the conditions for the implicit function theorem are satisfied. If so, write the equilibrium identity c. Find ??̅ ?? and discuss its economic implications

Labor Market Y = α (5N – 0.0025N2), where α = 2; N = labor The supply of labor, NS isNS = 55 + 10(1-t)w where t- tax rate = 0.5, w = real wage rate Good Market The desired consumption, Cd is Cd = 300 + 0.8(Y – T) – 200rWhere Y = income, T = taxes, r = real interest rate T= 20 + 0.5YG= 50Desired investment, Id:Id = 258.5 – 250r Money Market Demand for money, Md/P: Md/P = 0.5Y – 250(r + πe), where πe = 0.02 (expected inflation) Money supply = Ms = 9150 a)Find the equilibrium w, Y and N.b)Find the IS-curve and the equilibrium r, C and I.c)Find the LM-curve and the equilibrium P.d)If G increased to 72.5, find the equilibrium w, P, N, r, C and I.e)Discuss the differences between the equilibrium values in d) with a), b) and c). What is your conclusion with regard to the effectiveness of fiscal policy in this model?

Answer  1 st is incorrect.. don't use chat gpt please..give correct answer it's a last chance

first image is resource. questions starts in the second image (4. and 5.)