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Question 3 Three students have different demands for doughnuts. Andre's demand is given by Q-5-P Carlene's demand is given by Q-6-2P Cooper's demand is given by Q 4-0.5P. a. Derive the market demand curve for doughnuts algebraically. b. Graph the market demand curve for doughnuts. Pay special attention to any kinks in the market demand!

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Wade

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Step 1/2

a. The market demand curve is derived by summing the individual demand curves horizontally. This means that at a given price, we add the quantities demanded by each individual to find the total quantity demanded in the market.

Given the individual demand curves:

We sum these up to get the market demand:

`Q=Q_A​+Q_C​+Q_(C​^0`

Substituting the individual demands into this equation

`Q=(5-P)+(6-2P)+4-0.5P)`

Simplifying this equation gives us the market demand curve:

`Q=15-3.5P`

Explanation:

So, the market demand curve for doughnuts is `Q=15-3.5P` . This means that for each price level, the quantity demanded in the market is given by subtracting 3.5 times the price from 15.

Step 2/2

b. The market demand curve for doughnuts is `Q=15-3.5P`

`Q+3.5P=15`

`Q/15+P/(15/3.5)=1` ................................ intercept form of market demand

`P=0 , Q=15``P=4.2,Q=0` ........................... ( coordinates of market demand )

Explanation:

The following graph shows the market demand curve for doughnuts

Final Answer

a. The market demand curve for doughnuts is `Q=15-3.5P`

b. The following graph shows the market demand curve for doughnuts

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