4- 130 points] Assume that the demand line for a consumer is given by P-10-5Q. a

Question

4- 130 points] Assume that the demand line for a consumer is given by P-10-5Q. a- What is the slope of the demand? b- If the market price is P- 2. How much is the quantity demanded at this price? c- Calculate consumer total benefit, total spending, and surplus at the above mentioned price. d. Assume that market price changes form P:-2 to Pi-3, what is the elasticity of e-Now Assume that market price changes form P:-3 to P5-4. What is the f- How much is the consumers' willingness to pay for the 4th unit? demand? elasticity of demand?

Explanation / Answer

Answer 4

a) P = 10 - 5Q

Slope of Demand curve with Price on y axis and Quantity on x axis is given by:

dP/dQ = (-)5.

Hence slode of demand line = -5. Hence Demand is downward sloping

b) At P* = 2, Q = (1/5)(10 - P) = 8/5 = 1.6

Hence quantity Demanded =  1.6

c) Total spending is given by Price * Quantity demanded = 2*1.6 = 3.2

Hence Total Spending = 3.2

Consumer surplus = Benefit = Area below demand curve and above price line (P = 2) is given by:

At Q = 0, P =10 and at P = 2 Q = 1.6 Hence consumer surplus is given by:

Consumer surplus = (1/2)(1.6)(10-2) = 6.4

Hence Consumer Surplus = Consumer benefit = 6.4

d) elasticity of demand = (change in quantity/change in price)*(initial Price/initial quantity)

At P1 = 2 , Q1 = 1.6 and at P2 = 3 , Q2 = 1.4.

Hence Elasticity of demand = (Q2 - Q1)/(P2 - P1)(P1/Q1) = ((1.4-1.6)/(3-2))*(2/1.6)

= -0.2(2/1.6) = (-)0.25

Hence Elasticity of demand = (-)0.25

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