The equation for a demand curve has been estimate to be Q = 100 - 10P + 0.5Y, where Q is quantity, P is price, and Y is income. Assume that p = 7 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?
d. Now assume income is 70, what is the price elasticity at P = 8?
To answer my questions
a. The equation Q = 100 - 10P + 0.5Y represents a demand curve that shows the relationship between quantity demanded (Q) and two factors: price (P) and income (Y). The equation suggests that quantity demanded depends inversely on price (as price increases, quantity demanded decreases) and positively on income (as income increases, quantity demanded increases).
b. To calculate price elasticity at a price of 7, we need to use the formula:
Price Elasticity of Demand = (dQ/dP) * (P/Q)
Since the equation is given as Q = 100 - 10P + 0.5Y, we first differentiate with respect to P:
dQ/dP = -10
Substituting P = 7, we get:
Price Elasticity of Demand = (-10) * (7 / Q)
Therefore, we need the value of Q to calculate the price elasticity at a price of 7.
c. To calculate income elasticity at an income level of 50, we use the formula:
Income Elasticity of Demand = (dQ/dY) * (Y/Q)
Differentiating the equation Q = 100 - 10P + 0.5Y with respect to Y:
dQ/dY = 0.5
Substituting Y = 50, we get:
Income Elasticity of Demand = (0.5) * (50 / Q)
Again, we need the value of Q to calculate the income elasticity at an income level of 50.
d. Assume income is now 70 and P = 8. To calculate the price elasticity, we use the same formula as in part b:
Price Elasticity of Demand = (dQ/dP) * (P/Q)
Differentiating the equation Q = 100 - 10P + 0.5Y with respect to P:
dQ/dP = -10
Substituting P = 8, we get:
Price Elasticity of Demand = (-10) * (8 / Q)
Again, we need the value of Q to calculate the price elasticity at a price of 8, considering income is 70.
a. The equation Q = 100 - 10P + 0.5Y represents a demand curve. It shows the relationship between the quantity demanded (Q) and two factors: the price of the good (P) and the income of consumers (Y). The equation suggests that the quantity demanded (Q) is influenced by the price of the good (P) and the income of consumers (Y). A change in either the price or the income will affect the quantity demanded.
b. To calculate price elasticity, we need to differentiate the quantity (Q) with respect to the price (P) and then multiply it by P/Q. In this case, the equation for the demand curve is Q = 100 - 10P + 0.5Y. Differentiating Q with respect to P gives us -10. To calculate price elasticity, we need to multiply this by P/Q. Since we're trying to find the price elasticity at a price of 7, let's substitute P = 7 into the equation. So, price elasticity = -10 * (7/(100 - 10*7 + 0.5*50)).
c. Similarly, to calculate income elasticity, we need to differentiate Q with respect to Y and then multiply it by Y/Q. In this case, the equation for the demand curve is Q = 100 - 10P + 0.5Y. Differentiating Q with respect to Y gives us 0.5. To calculate income elasticity, we need to multiply this by Y/Q. Since we're trying to find the income elasticity at an income level of 50, let's substitute Y = 50 into the equation. So, income elasticity = 0.5 * (50/(100 - 10*P + 0.5*50)).
d. Assuming income is now 70 and price is 8, to find the price elasticity, we follow the same steps as in (b). Price elasticity = -10 * (8/(100 - 10*8 + 0.5*70)).