3 10 points Your firm MDF Corp is assisting the Marlboro Man

3. (10 points) Your firm, MDF Corp., is assisting the Marlboro Man in marketing their corn production. Yo are given the following supply function for the Southern regional corn market: Q, 9.5P-40 Qs is the quantity of corn supplied in 000\'s of bushel (bu) and P is the market price for corn $/bu. The current market price is $6.5/bu. a. At this price, what quantity of corn (in 000\'s) will the Marlboro Man supply to the b. At this market price level, is the supply of corn price elastic or price inelastic? MDF\'s marketing specialists have negotiated a new corn marketing contract with the market? following underlying corn supply function: Qs=12P-55 Under the new contract the contract price for corn changes to $6.20/bu c. What quantity of corn will the Marlboro Man supply? Has the elasticity of corn supply changed? If so, is it now more or less elastic than before the innovation? In terms of revenue, is the producer better or worse off after signing the marketing contract? Why or why not? d. e.

Solution

Qs = 9.5 P - 40

P = $ 6.5 per bushel.

(a) Qs = 9.5(6.5) - 40

= 61.75 thousands of bushels.

(b) Now, to calculate elasticity of supply , firstly take the first derivative of Qs with respect to P, we get:

Change in Qs/ Change in P = 9.5.

Elasticity of corn supply = (change in Qs / Change in P ) (P/Qs)

= 9.5 (6.5)/ 21.75

= 61.75/ 21.75 = 2.83 >0 .

It implies that the corn supply is price elastic.

When there is new marketing contract and supply is, Qs = 12P -55

And P = $6.20/ bushel

(c) By putting P in Qs , we get

Qs = 12(6.20) - 55

= 74.4 - 55 = 19.4 thousands of bushels.

(d) Elasticity of supply = (change in Qs/ change in P) (P/Qs)

Change in Qs / Change in P = 12 .

Elasticity = 12 (6.20) / 19.4 = 3.83 >2.83 >0

It implies that the elasticity of corn supply has changed . And now the supply of corn is more elastic.

(e) Total revenue before signing the contract = P(Q) = (6.5)(21.75) = 141.375.

Total revenue after signing the contract = P(Q) = (6.20)(19.4) = 120.28

It implies that the producer is worse off after signing the marketing contract as his producer surplus get reduced.