suppose that some market consists of 100 buyers and 10 sellers. Each buyer has a

Question

suppose that some market consists of 100 buyers and 10 sellers. Each buyer has an identical individual demand curve,
P=300-3Q
Each seller has an identical individual supply curve,
P=Q
The market demand curve will thus take the form P=a-bQ and the market supply curve will take the form P=cQ+d. In the following questions, I want you to solve for a, b, c, and d.

3. What is the value of the “a” term in the market demand curve?
4. What is the value of the “b” term in the market demand curve? (Use decimals. Round to two decimal places)
5. What is the value of the “c” term in the market supply curve? (Use decimals. Round to two decimal places)
6. What is the value of the “d” term in the market supply curve?

suppose that some market consists of 50 buyers and 100 sellers. Each buyer has an identical individual demand curve,
P=200-4Q
50 sellers have an identical individual supply curve,
P=Q+40
The remaining 50 sellers have identical supply curves equal to
P=Q+20
The market demand curve will thus take the form P=a-bQ and the market supply curve will take the form P=cQ+d (I want you to focus on the part of the supply curve where prices are such that all sellers are willing to sell the good). In the following questions, I want you to solve for a, b, c, and d.

7. What is the value of the “a” term in the market demand curve?
8. What is the value of the “b” term in the market demand curve? (Use decimals. Round to two decimal places)
9. What is the value of the “c” term in the market supply curve? (Use decimals. Round to two decimal places)
10. What is the value of the “d” term in the market supply curve?

Explanation / Answer

P=300-3Q This is inverse demand. Let's solve for demand. P=300-3Q Q = 100 - P/3 This is the quantity that each person will demand. So market demand is just 100 of these, Q = 10,000 - P*(100/3) But the question wants inverse market demand. P = 300 - 3Q/100 For supply: Q = P And there are 10 suppliers. So, market supply is: Q = 10P But the question wants inverse supply. P = Q/10 Inverse demand: P = 300 - 3Q/100 Inverse supply P = Q/10 The market demand curve will thus take the form P=a-bQ and the market supply curve will take the form P=cQ+d. In the following questions, I want you to solve for a, b, c, and d. 3. 300 4. 3/100 = 0.03 5. 1/10 = 0.1 6. 0 Now, we do the same thing only different :) P=200-4Q Q = 50 - P/4 Market demand is: Q = 2500 - P*(50/4) But the question wants inverse market demand: P = 200 - 4Q/50 50 sellers have P = Q + 40 and 50 have P = Q + 20 So... Q1 = P - 40 and Q2 = P - 20 Market demand: Q = 50*Q1 + 50*Q2 Q = 50P - 2000 + 50P - 1000 Q = 100P - 3000 But your question wants inverse market supply: P = Q/100 - 300 Inverse market demand: P = 200 - 4Q/50 Inverse market supply: P = Q/100 - 300 7. 200 8. 4/50 = 0.08 9. 1/100 = 0.01 10. 300

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