Solved Assignments [Requires calculus] Referring to Figure 8-5, show that if you cut marginal cost from $4.00 to…

  

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[Requires calculus] Referring to Figure 8-5, show that if you cut marginal cost from $4.00 to $2.00 you will raise output from 4 to 5 units and cut price from $8.00 to $7.00. Then show that you will pay up to $9.00 per year to invest in a lower-cost plant that lasts forever.a. Earlier you showed that if the original demand shifts upward by $2, and marginal cost remains , optimal output is 5 units and price is $9. Can you show algebraically that an upward demand shift of X dollars changes profit by the same amount as a downward marginal cost shift of X, assuming linear demand and constant marginal cost? b. Why do you expect that if marginal cost is upward-sloping your previous result will no longer hold? Or will it? Explain. c. If you face a relatively elastic demand, are your gains from a cost-reduction strategy greater or smaller than if demand is relatively inelastic? Explain in commonsense terms.

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