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)

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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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