The supply and demand for wheat are given by QS= 20 + 100p QD = 4000 - 100p +10Y

ID: 1256044 • Letter: T

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. Solve for the equilibrium price and quantity as functions of the consumer income.

b. Compute the derivative of quantity demand with respect to changes in average consumer income.

c. Compute the derivatives of the equilibrium price and quantity with respect to income.

Please show work step by step! Thank you!

QD = 4000 - 100P + 10Y

QS = 20 + 100P

(a) In equilibrium, QD = QS

4000 - 100P + 10Y = 20 + 100P

200P = 3,980 + 10Y

P = 19.9 + 0.05Y .... (1)

So,

Q = 20 + 100P = 20 + 100 x (19.9 + 0.05Y) = 20 + 1,990 + 5Y

= 2,010 + 5Y ......(2)

(b)

Derivative of quantity demanded with respect to income:

dQD / dY = 10

(c)

Derivative of equilibrium price with respect to income:

dP / dY = 0.05 [from part (a), equation (1)]

Derivative of equilibrium quantity with respect to income:

dQ / dY = 5 [from part (a), equation (2)]

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