The demand for a dozen ears of corn is$,$

$Q_{\text{C}\text{o}\text{r}\text{n}}^d=5-2P_{\text{C}\text{o}\text{r}\text{n}}+4P_{\text{P}\text{o}\text{t}\text{a}\text{t}\text{o}\text{e}\text{s}}-\mathrm{.}25P_{\text{B}\text{u}\text{t}\text{t}\text{e}\text{r}}+\mathrm{.}0003$I,

and the supply of a dozen ears of corn is$,$

$Q_{\text{C}\text{o}\text{r}\text{n}}^S=9+5P_{\text{C}\text{o}\text{r}\text{n}}-2P_{\text{F}\text{u}\text{e}\text{l}}-1\mathrm{.}25P_{\text{S}\text{o}\text{y}\text{b}\text{e}\text{a}\text{n}\text{s}}.$

Let the price of potatoes equal $$0\mathrm{.}50$ per pound, the price of butter equal $$4\mathrm{.}00$ per pound,

the price of fuel equal $$2\mathrm{.}50$ per gallon, the price of soybeans equal $$8\mathrm{.}00$ per bushel, and

consumer income equal $$30,000\mathrm{.}00$ per year.

a$.$ Calculate the equilibrium price of a dozen ears of corn and the market clearing

quantity of corn.

b$.$ Calculate the cross price elasticity of demand for potatoes at the equilibrium, interpret.

c$.$ Calculate the income elasticity of demand at the equilibrium, interpret.

d$.$ Graph the results from part a$.$

e$.$ Calculate the new equilibrium if the price of fuel increases to $$6\mathrm{.}00$ per gallon.

f$.$ Show the results in the graph.

g$.$ Calculate the total surplus in this market at the original equilibrium.