Use an isoquant drawing for the following problem:
Your firm uses machines and labor as inputs. Your firm also uses petroleum (oil) to run its machines. Your firm produces chocolate chip cookies. With L on the horizontal axis and K on the vertical, show where you might be in long run equilibrium at the production of 10,000 cookies. The price if L is "w", and the price of K is "r". Now:
In the SR, with L as a variable factor, where might you end up on the diagram if the w rises relative to r when you do not want your total costs to rise? What happens to the MPK in this case? Why? What happens to the MPL in this case? Why? Will you still be producing 10,000 cookies?
Is your new SR position efficient?
If you can wait for the LR, what will happen to the relative use if the two factors? What can you say abut the relative movements if the marginal products if the L and K, and what will be the relation between these marginal products and the prices of the factors?
Now go back to your original LR equilibrium position in the diagram. The price of oil rises. What do you expect to occur on your diagram in the SR and the LR? What happens to the MPK and MPK in these cases due to the oil price rise? If you want your costs to remain the same, will you still be producing 10,000 cookies.
Starting from the original equilibrium once again, you face a rise in the cost of L. However you want to continue to produce 10,000 cookies and minimize your costs at the sane time.
In the SR, where might you end up on the diagram with L as the variable factor? What happens to the ratios of MPK and MPL? Is this an efficient cost-minimum point?
As you move to the LR, and minimize your costs to produce 10,000 cookies, what does your diagram say abut the relative use if K and L, and what relation do their marginal products have with the prices of L and K?