. The supply and demand for wheat are given by QS = 20 + 100p QD = 4000 - 100p +
ID: 1136038 • Letter: #
Question
. The supply and demand for wheat are given by QS = 20 + 100p QD = 4000 - 100p +10Y Where Y is the average consumer income.
a. Compute the partial derivative of quantity demand with respect to changes in average consumer income. dQD/dA = 10
b. Solve for the equilibrium price and quantity as functions of the consumer income.
QS = QD: 20 + 100p = 4000 – 100p + 10Y 200p = 3980 + 10Y p*(Y) = 19.9 + 0.05Y Q*(Y) = 2010 + 5Y
c. Compute the derivatives of the equilibrium price and quantity with respect to income. dp*/dY = 1/20 dQ*/dY = 5
These are the questions and answers, I just need a very detailed explanation for each step because I do not seem to understand how we get those answers.
Explanation / Answer
(a) Qd = 4000- 100p +10Y
Partial derivative of Qd with respect to average consumer income is that dervative of Qd with respect to Y when all other variables are constant.
dQd/dY =10
(b) Qs = 20+100p
Qd= 4000-100p+10Y
To find equilibrium price and quantity, Equate Qd and Qs , we get:
20+100p= 4000- 100p+ 10Y
100p+100p= 4000-20 +10Y
200p = 3980 +10Y
p= (3980+10Y)/200
p*(Y)= 19.9 + 0.05Y (Equilibrium price )
Put p= 19.9+ 0.05Y in any of quantity equation , we get:
Q= 20+ 100(19.9 +0.05Y)
Q= 20+ 1990 +5Y
Q* = 2010 +5Y (Equilibrium quantity)
(c) Equilibrium price : p*=19.9 +0.05Y
Derivative of the equilibrium price with respect to income is:
dp*/dY = 0.05 = 5/100 =1/20
Equilibrium quantity : Q*= 2010+5Y
Derivative of quantity with respect to income is:
dQ*/dY = 5
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