4. Considerthe following firm‐levelsupply schedule for oranges:
q = f(P) = 2P ‐ 2, where P= themarket price of oranges.
a. Ifthere are 10 identicalfirmsin themarket,then whatisthe equation forthemarketsupply
schedule (Q)? Find the derivative ofmarketsupply with respectto price when there are 10
firms.(5 points)
b. Suppose there areNfirmsin themarket. Whatisthe equation formarketsupply? Find the
partial derivative ofmarketsupply with respectto price. Verify thatthis equation isthe same
as above whenN=10.(5 points)
c. Sketch themarketsupply schedule in a diagramwhenN=10; be sure to identify the vertical
intercept and the slope ofthe supply schedule in your diagram(HINT:mind your P’s andQ’s!).
Verify in your diagramand using calculusthatthismarketsupply schedule obeysthe law of
supply.(5 points)
Part Four: Market Equilibrium
5. Using themarket demand and supply functionsfromquestions 3 and 4 (respectively);find
the equilibriumprice and quantity traded whenN=10 and I=10. Show your work. (5 points)
6. Suppose consumerincome decreasesto I=5; find the new equilibriumprice and quantity
traded. Show your work.(5 points)
7. In a well‐labeled diagram, illustrate the effect onmarket price and quantity of a decrease in
consumerincome on themarketfor oranges(i.e.,the scenario in questions 5&6, above).
However, you do not need to label any intercepts orslopes, justthe original and new
equilibriumprices and quantities.(5 points)
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