Question: The Demand and Supply functions for pork in the textbook example were:

\[\begin{aligned} & {{Q}^{D}}=171-20p+20{{p}_{b}}+3{{p}_{c}}+2Y \\ & {{Q}^{S}}=88+40p \\ \end{aligned}\]

a. What is the inverse demand function for pork and how much would the price have to rise for consumers to want to buy 2 million fewer kg of pork per year.

b. If the price of beef, p_b = $4/kg and the price of chicken p_c = $3 1/3 / kg and income

Y = 12.5 (in thousands of $), show how the equilibrium quantity of pork varies with income. Hint: Your answer must be a function of Y.

c. Show the effect of a decrease in income on the equilibrium using a well-labeled graph.