Question

The supply of wheat is given by the following equation:QWS = –6 + 4Pw – 2Pc –Pf
where QWS is the quantity of wheat supplied, in millions of bushels;Pw is the price of wheat per bushel;
Pc is the price of corn per bushel; and Pf is the price of tractor fuel per gallon.

a. Graph the inverse supply curve when corn sells for $4 a bushel and fuel sells for $2 a gallon.
What is the supply choke price?
b. How much wheat will be supplied at a price of $4? $8?
c. What will happen to the supply of wheat if the
price of corn increases to $6 per bushel? Explain
intuitively; then graph the new inverse supply
carefully and indicate the new choke price.

Answer 1

(a) Plugging in given values,

QWS = – 6 + 4Pw – 2Pc – Pf = - 6 + 4Pw - (2 x 4) - 2 = - 6 + 4Pw - 8 - 2

QWS = - 16 + 4Pw

4Pw = QWS + 16

Pw = 0.25QWS + 4 (Inverse supply function)

When QWS = 0, Pw = $4 (supply choke price and vertical intercept of supply curve).

In following graph, S0 is inverse supply curve.

(b) QWS = - 16 + 4Pw

When Pw = $4, QWS = - 16 + (4 x 4) = - 16 + 16 = 0

When Pw = $8, QWS = - 16 + (4 x 8) = - 16 + 32 = 16

(c) When Pc = 6, supply for wheat will decrease, since Pc has a negative coefficient in supply function, indicating inverse relationship between Pc and QWS.

QWS = – 6 + 4Pw – 2Pc – Pf = - 6 + 4Pw - (2 x 6) - 2 = - 6 + 4Pw - 12 - 2

QWS = - 20 + 4Pw

4Pw = QWS + 20

Pw = 0.25QWS + 5 (Inverse supply function)

When QWS = 0, Pw = $5 (new supply choke price and vertical intercept of new supply curve).

In above graph, S1 is new inverse supply curve.