12. You are told that Mouliya purchases 10 oranges when the price of each orange is $0.20. You also know that for every $0.10 increase in price Mouliya purchases one less orange. Mouliya's demand curve is linear. i. In the space below draw a sketch of Mouliya's demand curve given the above information. Your sketch should identify two points that lie on this demand curve (give numerical values for the coordinates of these two points). Your sketch should have both axes labeled as well as the demand curve. Price of Oranges. $0.30 $0.20 (9,$0.30) 9 10 (10, $0.20) Demand Quantity of Oranges ii. Given the above information write an equation for Mouliya's demand curve for oranges using P as the symbol for the price per orange and q as the symbol for the quantity of oranges demanded by Mouliya. For full credit show your work in deriving this equation. iii. Suppose there are twenty individuals in all (including Mouliya) in this market and all of these individuals have identical demand curves based on the information you were given about Mouliya. Provide a verbal explanation of how you would find the market demand curve. iv. Find this market demand curve using P as the price per orange and Q as the total quantity demanded by these twenty individuals. (Hint: you may find it helpful to draw a sketch of Mouliya's demand curve and a separate sketch of the market demand curve.) Show your work to get full credit.
12.
i.
In the graph below, price on Y axis and quantity demand on x axis.
When price is 0.20 then quantity demand is 10 oranges.
When price rises by 0.10 then quantity demand decreases by 1 unit. Then if price is 0.30 then quantity demanded is 9 oranges.
ii.
Demand curve equation:
P= a-bq
When P= 0.20, q= 10:
0.20= a-10b equation 1
When P= 0.30, q= 9:
0.30= a-9b equation 2
Subtract equation 2 from 1:
a-10b-a+9b= 0.30-0.20
-b= 0.10
b= 0.10
Use this value in equation 2:
a-9(0.10)= 0.30
a-0.9= 0.3
a= 0.30+0.90= 1.20
Demand equation:
P= 1.20-0.10q
iii.
Market demand is the sum total of individual demand for all the consumers. The market quantity is the sum of individual quantity or multiplier individual quantity by number of consumers.
iv.
P= 1.20-0.1q
0.1q= 1.20-P
q= 12-10P
Q= number of consumer x q
Q= 20(12-10P)
Q= 240-200P
200P= 240-Q
P= (240-Q)/200
When Q=0, P= 1.2 and when P= 0, Q= 240:
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