Suppose, to benefit soy farmers harmed by a drop in demand for soybeans the government was to institute a price floor setting the minimum price of soy beans at $12 per bushel. Use the graph below to answer the following questions regarding the price floor. Soybean Market Price (Per Bushel) $20 $16 $12 $8 $4 0 10 20 30 40 50 Supply Demand Quantity (Thousands of Bushels) (a) Prior to the institution of price floor, what was the equilibrium price of a bushel of soybeans? [ Select ] (b) Does the institution of a price floor increase or decrease the quantity of soybeans demanded? [ Select ] (c) Does the institution of a price floor create a shortage or a surplus in the market for soybeans? [ Select ] (d) How many fewer soybeans are sold after the price floor was put in place than were sold without the price floor? [ Select ]
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One area where the law of supply and demand is clearly at work is farm commodities. Both growers and consumers watch this relationship closely, and use data collected by government agencies to track the relationship and make adjustments, as when a farmer decides to convert a large portion of her farmland from corn to soybeans to improve profits. Suppose that for $x$ billion bushels of soybeans, supply is modeled by $y=1.5 x+3,$ where $y$ is the current market price (in dollars per bushel). The related demand equation might be $y=-2.20 x+12 .$ (a) How many billion bushels will be supplied at a market price of 5.40 dollars? What will the demand be at this price? Is supply less than demand? (b) How many billion bushels will be supplied at a market price of 7.05 dollars? What will the demand be at this price? Is demand less than supply? (c) To the nearest cent, at what price does the market reach equilibrium? How many bushels are being supplied/demanded?
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The following tables give price-demand and price-supply data for the sale of soybeans at a grain market, where $x$ is the number of bushels of soybeans (in thousands of bushels) and $p$ is the price per bushel (in dollars): $$ \begin{array}{cccc} \hline \multicolumn{2}{c} {\text { Price-Demand }} & \multicolumn{2}{c} {\text { Price-Supply }} \\ x & p=D(x) & x & p=S(x) \\ 0 & 6.70 & 0 & 6.43 \\ 10 & 6.59 & 10 & 6.45 \\ 20 & 6.52 & 20 & 6.48 \\ 30 & 6.47 & 30 & 6.53 \\ 40 & 6.45 & 40 & 6.62 \\ \hline \end{array} $$ Use quadratic regression to model the price-demand data and linear regression to model the price-supply data. (A) Find the equilibrium quantity (to three decimal places) and equilibrium price (to the nearest cent). (B) Use a numerical integration routine to find the consumers' surplus and producers' surplus at the equilibrium price level.
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