Consider again the function for the demand for sugar presented in question 6 of
ID: 1201192 • Letter: C
Question
Consider again the function for the demand for sugar presented in question 6 of Section 8.2, Q_d = f(Y,P_c,P_s) = 0.05Y + 10P_C - 5P^2_s, where Q_d is the demand for sugar, Y is income, P_s is the price of sugar, and Pc is the price of saccharine. Use the total differential to find the approximate change in the demand for sugar with an increase in income of $1 if, initially, Y = 10,000, P_s, an P_c = 7. Use the total differential to find the approximate change in the demand for sugar with a $1 increase in the price of sugar if, initially, Y = 10,000, P_s = 5, and P_c = 7.Explanation / Answer
Qd = 0.05Y+10Pc-5Ps2
a)
The effect of increase in income on the total demand for sugar can be calculated by finding out the differential of Qd with respect to Y
That is,
dQ/dY = 0.05
Thus, increase in QD because of increase in income by $1 will be 0.05
b)
Similarly, the effect of increase in price of sugar on the total demand for sugar can be calculated by finding out the differential of Qd with respect to Ps
That is,
dQ/dPs = -10Ps
Thus, decrease in QD because of increase in price of sugar by $1 will be 10×(average of 5 and 6) = 55