4. The equation for a demand curve has been estimated to be Q = 100 – 10P + 0.5Y where Q is quantity, P is price, and Y is income. Assume that P = 7 and Y = 50.
a. Interpret the equation.
b. What is price elasticity at P = 7 and arc elasticity at the interval between P = 6 and P=7.
c. What is income elasticity at Y = 50 and arc elasticity at the interval between Y = 50 and P=60.
d. Now assume that income is RM70. What is the price elasticity at P = 8? Also, calculate arc elasticity at the interval between P=7 and P= 8.
A. Q=100-10*7 +0.5*50
Q= 100-70+25
Q= 55
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The equation for a demand curve has been estimated to be Q = 100 - 10 P + 0.5 Y, where Q is quantity, P is price, and K is income. Assume P = 7 and Y = 50.
a. Interpret the equation.
b. At a price of 7, what is price elasticity?
c. At an income level of 50, what is income elasticity?
a. The demand curve equation, Q = 100 – 10P + 0.5Y, represents the relationship between the quantity demanded (Q) and the price (P) and income (Y). It shows how changes in price and income affect the quantity demanded. Specifically, the equation implies that for every one unit increase in price (P), the quantity demanded (Q) decreases by 10 units, and for every one unit increase in income (Y), the quantity demanded (Q) increases by 0.5 units.
b. To calculate price elasticity of demand at P = 7, we need to determine the percentage change in quantity demanded when the price changes by 1 unit. The formula for price elasticity of demand is:
Price elasticity of demand = (percentage change in quantity demanded) / (percentage change in price)
Considering P = 7 and changing it to P = 6, we can calculate the percentage change in quantity demanded as follows:
Percentage change in quantity demanded = [(Q at P = 6) - (Q at P = 7)] / (Q at P = 7) * 100
Substituting the values into the equation, we get:
Percentage change in quantity demanded = [(100 – 10(6) + 0.5(50)) - (100 – 10(7) + 0.5(50))] / (100 – 10(7) + 0.5(50)) * 100
Simplifying the equation will give us the percentage change in quantity demanded.
To calculate arc elasticity at the interval between P = 6 and P = 7, we take the average of the price elasticity at P = 6 and the price elasticity at P = 7.
c. To calculate income elasticity of demand at Y = 50, we need to determine the percentage change in quantity demanded when income changes by 1 unit. The formula for income elasticity of demand is:
Income elasticity of demand = (percentage change in quantity demanded) / (percentage change in income)
Similarly, we can calculate the percentage change in quantity demanded at the interval between Y = 50 and Y = 60 using the same formula as mentioned above.
d. To calculate the price elasticity of demand at P = 8 with income at RM70, we use the same formula:
Price elasticity of demand = (percentage change in quantity demanded) / (percentage change in price)
Similarly, we calculate the arc elasticity at the interval between P = 7 and P = 8 by taking the average of the price elasticity at P = 7 and the price elasticity at P = 8.