Macroeconomics 12th Edition by Rudiger Dornbusch ,Stanley Fischer,Richard Startz

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Consider a production function of the form Y = AF ( K, N, Z ), where Z is a measure of natural resources used in production. Assume this production function has constant returns to scale and diminishing returns in each factor.
a. What will happen to output per head if capital and labor both grow but Z is fixed
b. Reconsider part a, but add technical progress (growth in A ).
c. In the 1970s there were fears that we were running out of natural resources and that this would limit growth. Discuss this view using your answers to parts a and b.