Suppose there has been a storm in Nebraska that has destroyed part of the corn crop in the field. The demand curve for corn has not changed. As a result, the market clearing prices and quantities before and after the storm are: Pb = 50, Qb = 2000; Pa = 100, Qa = 1500. (The subscripts a and b refer to “after the storm” and “before the storm”.) 

a. Assume a linear demand curve for corn, i.e. P = α + β Q. Calculate α, β with the provided information, and draw the demand curve with P on the y-axis and Q on the x-axis. Label the intercept and the slope on the graph.

b. The supply curve for the period after the storm is P = (1/15) Q, and it is parallel to the supply curve before the storm. Is the supply curve before the storm above or below that after the storm? Calculate the slope and the intercept of the supply curve before the storm. Draw both supply curves on a new graph with P on the y-axis and Q on the x-axis. Add the demand curve (calculated in part a) to the graph. 

c. Suppose consumers care only about corn consumption and apple consumption (they live in a two-good world). How would the change in the price of corn affect the budget constraint of the typical consumer? Show graphically. How would the change in relative prices affect the typical consumer’s consumption of corn versus apples? Is this result consistent with your observation from the demand and supply framework (i.e. an increase in price of corn is associated with a decrease in the equilibrium quantity)? Explain.