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Page 1 of 2 ZOOM + exhibits 1. constant returns to scale and ii. diminishing returns to capital (K) and labor (N). 2. 15 POINTS Suppose that the consumer's optimization problem is given by max In(c) + yln(1) subject to Pc + (1 - t)Wl = (1 - t)Wh + II a) Write the Lagrangian and take the first order conditions. b) Use the first order conditions to derive the solution for c* and 1*. c) Using the equations for c* and 1*, show what happens when there is a decrease in the tax rate t. Using graphs similar to those in Lecture 3, also show what happens to c* and 1* graphically. d) Now show what happens to c* and 1* (both mathematically and graphically) if at the same time, the tax rate t decreases and the nominal profits II decrease