This problem will require that your review the discussion of marginal revenue product (MRP) and profit maximization at pages 389-93 / 381-85 (not including the "A mathematical development" section).It will make you a Better Person.Part (a) is already done; be sure that you understand it before proceeding.

b)Let's demonstrate the preceding point with an example.For w = $5, r =$15, a production function q = 4 L^0.5+ 12 K^0.5, and a constant price of $50 per unit of q, solve for L and K based on the MRP rules at 11.45 and 11.46, showing your work.(You should get 400 for each.)Then, using the values you found, demonstrate that the last dollar rule holds.Finally, show that q = 320, given the L and K that you found.

c)For an output q = 320 and the above production function, solve for L, K and the minimum expenditures using the production function and the RTS = w/r condition.(In other words, solve the constrained minimization problem.)

d)Suppose now that a firm has output q = 100 with the above production function, input prices, and output price.Calculate L and K (you might see a shortcut), and show that the firm is not complying with the MRP conditions.How should it change its behavior?

e)Equation 11.47 is satisfied for this production function; for example,

f_LL= -L^-1.5< 0.Given this, satisfying equation 11.48 is not a concern at all for this production function.Why not?(You can explain in words (one or two sentences) or show the math.) Would these concerns matter for a Cobb-Douglas function?

The remainder of this problem examines how L and K respond to a change in w.

Fix K at 400; it cannot vary.Let the wage rate w fall from $5 to $4.Read the "Input Demand Functions" and the "Single-input case" sections at pages 391-92/383.Equation 11.50 is setting up a level set for profit using the MRP rule, which now involves only one variable.That is, given fixed w and P, and in the background fixed K, equation 11.50 gives the profit maximizing level of L.Equation 11.51 is then using this notation to determine how use of L will change as w changes, from a starting point of profit-maximizing usage of L; the point is that L will not move in the same direction as w.

f)Solve for the new level of L at w = $4.

g)Now let K and L both vary and use the facts of part (b) to solve for K and L, but with the sole change that w = $4.Compare your results to (f).Read the "Two-input case" section at p. 391/383 and briefly explain why the concerns it raises are not a problem for this production function.

The remainder of this problem examines how L and K respond to a change in w.

Please help me to answer question e, f, g