Y=KANBN+CL

Ystands for output,Kstands for the capital stock,Nstands for the number of people employed,Lstands for the quantity of land used in production,AandBstand for measures of labour efficiency, andCfor a measure of land efficiency.is a parameter whose value is between 0 and 1,andare parameters whose values are1.

(a) Derive the formulas for:

- the marginal product of labor (MPN).

- the marginal product of capital (MPK). - the marginal product of land (MPL).

(b) Using calculus derive a formula for the aggregate labour demand (ND). Express aggregate labour demand as a function of the real wagew(and all other variables and parameters).

(c) The aggregate quantity of labor supplied isNS= 50 + (1 +s)w, wheresis a wage subsidy paid by the government. Assume thats= 1, A= 100, B= 1/4,K= 1,= 2: solve for the equilibrium real wage (w), full-employment level (N). Assume thatL= 10,C= 1 and= 2: find the full-employment level of output (Y).

(d) The government's goal is to achieve the employment levelN= 100: what is the value of the subsidysthat is needed in order to reach this target? What are the implied wagewand outputY? Comment on your findings.