Question

Much of the demand for U.S. agricultural output has come from other countries. In \(1998,\) the total demand for wheat was \(Q=3244-283 P .\) Of this, total domestic demand was \(Q_{D}=1700-107 P,\) and domestic supply was \(Q_{s}=1944+207 P .\) Suppose the export demand for wheat falls by 40 percent. a. U.S. farmers are concerned about this drop in export demand. What happens to the free-market price of wheat in the United States? Do farmers have much reason to worry? b. Now suppose the U.S. government wants to buy enough wheat to raise the price to \(\$ 3.50\) per bushel. With the drop in export demand, how much wheat would the government have to buy? How much would this cost the government?

Short answer

Based on the solutions from the steps above, the short answer includes new equilibrium price of wheat obtained from step 3. Depending on that price, the farmers' concerns are analysed. Furthermore, the quantity of wheat that the government needs to buy to raise the price and the associated expense is also calculated.

Step-by-step solution

Calculating the New Total Demand

To calculate the new total demand, subtract 40% of the original total quantity demanded (because export demand falls by 40 percent) from the total quantity demand. Thus, the equation for the new total demand \(Q_{N}\) is given by: \(Q_{N}=Q-0.4(Q_{D})\)

Establishing The New Equilibrium

Next, set the new total demand equal to the supply in order to find the new equilibrium price. Therefore: \(1944+207P =3244-283 P-0.4(1700-107P)\)

Solving For The Equilibrium Price of Wheat

Solving the equation established in step 2 will give the new equilibrium price of wheat. Utilize algebraic methods to solve for \(P\).

Analyzing Farmers' Concerns

Depending on whether the price falls or rises, provide explanation regarding the farmers' concerns. A falling price means less revenue for farmers, which could be a great cause of concern.

Price Determination By Government

To calculate the quantity of wheat the government needs to buy, fill in the price \(P=3.50\) in the new demand equation we got before. The equation now is: \(Q_{N}=3244-283*3.50-0.4*(1700-107*3.50)\)

Calculating The Wheat Quantity

The solution for the above equation gives the quantity that the consumers will demand at that price. However, the government wants to artificially set the price to $3.5. To do this, it needs to buy the surplus from the market, which can be calculated by subtracting the quantity demanded from the quantity supplied. Hence we have \(Q_{s}-Q_{N}\)

Calculating Government's Expense

The cost to the government is the wheat quantity it must buy multiplied by the price ($3.50) per bushel that it sets, which is \(expense = quantity*3.50\)

Key concepts

Export Demand for Agricultural Products

Understanding how export demand affects agricultural markets is crucial for grasping global trade dynamics. For instance, U.S. farmers producing wheat are significantly impacted by changes in export demand. When there's a high demand for wheat internationally, this can lead to an increase in wheat prices due to higher overall demand. However, if export demand falls, as indicated in our exercise by a 40% drop, this leads to a surplus of wheat on the domestic market, driving prices down.

Farmers exporting wheat would indeed have reason to worry in this scenario. The fall in export demand would mean that they might have to sell their wheat at lower prices, which could affect their income and profitability. Changes in export demand could come from various factors, including shifts in international market preferences, changes in trade policies, or global economic trends.

Market Equilibrium

Market equilibrium occurs when the quantity of a product demanded by consumers equals the quantity supplied by producers, resulting in a stable market price. In the ideal free-market scenario, equilibrium is naturally achieved without intervention as suppliers and consumers interact.

Taking the information provided in the exercise, the equilibrium price is determined by setting the total demand for wheat equal to the total supply. When these two forces are imbalanced, as in the case of a sudden drop in export demand, the equilibrium price will shift. A lower export demand translates to a decrease in the overall market price of wheat, if supply remains constant. This can be particularly harmful to farmers if the equilibrium price falls below their production costs, leading to potential financial strain.

Government Market Intervention

In instances where the free-market equilibrium is not favorable for a critical sector, such as agriculture, governments may intervene to stabilize prices. One method of intervention is purchasing surplus stock, as described in the step-by-step solution. If the government wants to maintain the wheat price at $3.50 per bushel, it must buy the excess wheat after the export demand drops.

By setting a minimum price threshold, the government ensures that farmers still receive a certain income for their crop, preventing the market price from falling below a level that would cause economic harm to the agricultural sector. This intervention has a cost associated with it, as the government must use taxpayer money to purchase and possibly store the surplus wheat, which, as the exercise outlines, is found by multiplying the surplus quantity by the set price per bushel.