Question

Consider the following supply and demand model derived from a small farming town

             qCD=.5I-.1PC          (1)

             qCS=1.9PC+5R $KMwb++qYAAAAASUVORK5CYII=$          (2)

Where equation (1) denotes the monthly demand for corn and equation (2) denotes the monthly supply for corn. (PC) is the price of corn, (I) denotes average consumer income, and (R) denotes average monthly days of rainfall.

17. Based on the supply and demand model depicted in equations (1) and (2):
    1. If average monthly consumer income is 200 and average rainfall per month is about 10 days, solve for the equilibrium market price and quantity. Plot the supply and demand functions (label your graph and show the symbolic equilibrium market price and quantity). What is the price elasticity of supply and demand at the equilibrium price? How do they compare?
    2. A new leadership arose and so did the government policies towards farmers. Thus, a new law is being proposed aimed at generating more revenue for the state. The government is now considering taxing farmers by an amount of $ 3 dollars per each bushel of corn sold. If average consumer income and rainfall remain the same, demonstrate what would happen to the market if the state approved the tax plan (use a supply and demand diagram and label your curves and axis properly). How much revenue will the government generate? If a core objective of the government is to avoid a 2 percent decrease in production following the tax plan, would you consider this plan to be unsuccessful? Who is likely to absorb the highest burden of the tax? (consumers or producers? You can think about this in term of elasticity or how much consumers will pay or how much producers will receive after the tax is imposed).
    3. (No tax scenario), all the sudden a drought occurs, and the average days rainfall drops to 2, while consumer income remain unchanged, demonstrate what will happen in the market (plot the new changes using a supply and demand diagram; again label your curves and axis properly). In the following month, your chief economist proposes two stabilization packages to absorb the shock: (i) the imposition of a $ 20 price ceiling to force lower prices in the market; or a subsidy of $ 20 for each bushel of corn sold; so as to minimize the impact of the drought on farmers revenues. As the governor, which policy would you select? Whatever case you decided to choose, you need to show the resulting outcome of the policy on the market (use a supply and demand diagram, including some arithmetic to defend your point of view). You must choose one of the two policies.

Answer 1

A)

q1a equilibruin at = des 0.58200-0.18 = 1.9 Pc+5x10 100-50= 2 Pc Pcz 7 = 25 Q = A p = 0.5X200-0:1X25 deda aso 100-25=97.5

libruing supply Bolle 25 demanet have O So 97.5 100 Quantity

3. व -0.) x2) -95--00 0 256 sxe .x25 -0.48 Ale

B)

After 3 $ tux New supply tune now sol coauts to sell each quantity ent 38 ore than before Q = 7.9 Pc + 50 = 109 (123) +50=log Pe +44.3 &cs- 8cd 1.99 +44.3=100-0-1 Pc Pc = 55.7 = 27.85 7.85 +4 40.3=97.215

- Pemene cuilibu Juwsupply 27.857 = Initial supsty 44.3 50 94.215 iro Tax revenu = 34 97.215=291.645 Production decreased = 0.285 x 100 = 0.292% 52% Plan is successfull. 97.5

Consumm burden of fax = New Pt - old to = 27.85-25 = 2.85 producer's burless = Tax - Consumer's burdens = 3-2.85-0015 do Consumer absorb most of the tax burden

C)

reun dags Newsypply function Afert e o I fell to 2 days, Az %9 pe +5x2= 1-9 petto New equilibrary 1.98 Ho=100-O-IP P = 90 P = 45 Pcd = 0,5 = 100-031x45= 0 955 Nadsupply old supply 10 so 95.5 57.25

At 20 P=20$ del = 100-00/X20=98 TR = 20x98 = 19.60 After Subsidy of 208, New Demand function del = 100 - Oolle 20) = 100 -0.1P + 2 = 102-0-1 Pe - New equilibrium 102-0-1P = 1.9 p. to 92 - 2 P P = 46 102-00)x46=102-406 = 97.4 TR = 9704x46=4480.4 So 208 subsidy is better to quercase Total revenue of fermus.