Could somebody please do this problem for me. I would like tosee it done so I can understand the process. I have a test on thismaterial coming up real soon and would like to see this done. Thankyou!!
Problem 1: Firm Behavior: Consider a firm whose productionfunction is of the form
yt =Atkt1/4nt3/4
where yt is real output in period t, kt iscapital input in period t, and nt is labor input inperiod t. The price of output is 1 and let all variables, includingwages and interest rates be in real terms. The firm is infinitelylived. At is total factor productivity of the firm inperiod t, which is exogenous to the firm. Assume that Atgrows at rate a, that is, At+1 = (1 + a)At;where A0 (that is, At at time 0) is 1.
a. Based on the two-period model covered in class, write down thefirms budget constraint in period t.
b. Derive the firm's demand for labor in period t as a function ofwages, interest rates and a.
c. Derive the firm's demand for investment (not kt butthe change in kt) in period t as a function of wages, interest rates and a.
d. Explain briefly how an increase in a would change your answers in parts b and c.