Katherine has an estimated Cobb-Douglas utilityfunction of U = q1^0.25q2^0.75 for food, q1, and housing, q2. Theprice for food is arbitrarily set at $1 per unit and the averagemonthly rent near the University of Chicago , p2, is a dollar fiftyper square foot. Caroline, like the average University of Chicagostudent spend $750 on food and housing per month.
    (a) Using calculus, solve forKatherine's optimal quantities of housing and food. Provide themarginal utility of income.
    (b) What is Katherine'sutility at the optimal bundle?
    (c) Due to panic buying andlogistical difficulties due to the coronavirus, suppose theper-unit price of food increases by 25% (p1= $1.25), what isKatherine's new utility facing this price increase?
    (d) How much money wouldKatherine need to completely offset the harm from the priceincrease?
    (e) How much money would onehave to take from Katherine to harm her as much as the priceincrease?
