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Question
1. Three students have different demands for doughnuts. André'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!

Asked By MysticMoon98 at

Answered By Expert

Neil

Expert · 3.7k answers · 3k people helped

Step 1/3

(a) We know that,

`Market \ dem a n d \ curve = Sum \ of \ i n d ividual \ dem a nd` `Q_d = Q_a + Q_b + Q_c ` `Q_d = 5 - P + 6 - 2P + 4 - 0.5P `

`Q_d = 15 - 3.5 P `

Explanation:

Accordingly, From the given data we obtain that,

Explanation:

Explanation:

Hence demand curve is,

Explanation:

Explanation:

`Q_d = 15 - 3.5 P `

Step 2/3

(b) As obtained above, the Market demand curve for doughnuts is as follows:

`Q = 15 - 3.5P` Now, For plotting graph: `Q + 3.5P = 15` `\Rightarrow \frac{Q}{15} + \frac{P}{\frac{15}{3.5}} = 1`

`\Rightarrow \frac{Q}{15} + \frac{P}{4.28} = 1` `\Rightarrow ` Intercepts form of market demand.

Explanation:

Using:

Explanation:

Explanation:

`\Rightarrow \frac{Q}{15} + \frac{P}{4.28} = 1 `

Explanation:

Explanation:

Thus, the Intercepts of the axis are:

Explanation:

Explanation:

P = (0, 4.8), Q = (0, 15)

Step 3/3

The graphical representation is as follows:

In which:

AB = Market demand for doughnuts.

Explanation:

As obtained above

Explanation:

Explanation:

The Intercepts of the Axis:

Explanation:

Explanation:

P = (0, 4.8), Q = (0, 15)

Final Answer

(a)

`Q_d = 15 - 3.5 P `

(b) P = (0, 4.8), Q = (0, 15)

The graph is illustrated above

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