1. (30 pts) The wheat market has the following supply and demand functions p-98-
ID: 1133691 • Letter: 1
Question
1. (30 pts) The wheat market has the following supply and demand functions p-98-4P+0.21 Where Pw is the price of wheat (per bushel), O is the quantity of wheat in bushels, I is the average consumer's daily income, Pc is the price per bushel of corn, and Pris the price of tractor fuel per gallor. a. (5 pts) Using the supply and demand equations for wheat, solve for the equilibrium price and quantity of wheat as functions ofI, Pc, and Pr b. (5 pts) Assume that the consumers' daily income is $200, the price per bushel of corn is $4, and the price of tractor fuel $2 per gallon. Derive the equations for the demand and the inverse demand curves. Draw this demand labeling as many points as you can. Indicate the regions where the demand is elastic, unit elastic, and inelastic (5 pts) Assume that the consumers' daily income is $200, the price per bushel of corn is $4, and the price of tractor fuel S2 per gallon. Derive the equations for the supply and the inverse supply curves. Draw this supply labeling as many points as you can. c. d. (5 pts) Assume that the consumers' daily income is $200, the price per bushel of corn is $4, and the price of tractor fuel $2 per gallon. Using calculus and the equations you obtained in part a, determine how the equilibrium price and quantity vary when I, Pc, and Pr increase, one at a time. Show each of these effects graphically in a supply and demand model (5 pts) Assume that the consumers' daily income is $200, the price per bushel of corn is $4, and the price of tractor fuel S2 per gallon. Compute the own price elasticity of demand at the equilibrium price and quantity. What would happen to the revenue of a firm if the price of wheat went down? Why? e. f. (5 pts) Assume that the consumers' daily income is $200, the price per bushel of corn is $4, and the price of tractor fuel S2 per gallon. Compute the Income elasticity of demand. Is wheat normal or inferior? Why? How much would income have to change in order to increase the demand of wheat by 5%?Explanation / Answer
Qd = 98 - 4Pw + 0.2I
Qs = -6 + 4Pw -2Pc - 2Pf
a) Qd=Qs.
98 - 4Pw + 0.2I = -6 +4Pw - 2Pc - 2Pf
104 = 8Pw + 0.2I - 2Pc - 2Pf
Pw = 13 + 0.025I - 0.25Pc - 0.25Pf
Q = 98 - 4*(13 +0.025I - 0.25Pc - 0.25Pf) +0.2I
Q = 98 - 52 - 0.1I + Pc +Pf + 0.2I
Q = 46 - 0.1I + Pc + Pf
b) Qd =98 - 4Pw + 0.2I
Qd = 98 -4Pw + 0.2*200
Qd = 138 - 4Pw .
inverse demand curve. Pw = 134.5 - 0.25Qd
C) Qs = -6 + 4Pw -2Pc - 2Pf
Qs = -6 + 4Pw - 2*4 - 2*2
Qs = -6 +4Pw - 8 -4
Qs = -18 + 4Pw
or inverse supply curve.
Pw = 4.5 + 0.25Qs
d) Pw = 13 + 0.025I - 0.25Pc - 0.25Pf
Pw = 13 + 0.025*200 - 0.25* 4 - 0.25*2
Pw = 13 +5 - 1 -0.5
Pw = 16.5
Qd = 138 - 4Pw
Qd = 138 -4*16.5
Qd = 72
suppose I becomes $400 now.
Pw = Pw = 13 + 0.025I - 0.25Pc - 0.25Pf
Pw = 13 + 10 - 1-0.5
Pw = 21.5
Qd = 98 - 4*21.5+ 0.2*400
Qd = 92
e) , F0 and G) please upload it againt. it against chegg policy.
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