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In: Economics

Katherine has an estimated Cobb-Douglas utility function of U = q1^0.25q2^0.75 for food, q1, and housing,...

Katherine has an estimated Cobb-Douglas utility function of U = q1^0.25q2^0.75 for food, q1, and housing, q2. The price for food is arbitrarily set at $1 per unit and the average monthly rent near the University of Chicago , p2, is a dollar fifty per square foot. Caroline, like the average University of Chicago student spend $750 on food and housing per month.

     (a) Using calculus, solve for Katherine's optimal quantities of housing and food. Provide the marginal utility of income.

     (b) What is Katherine's utility at the optimal bundle?

     (c) Due to panic buying and logistical difficulties due to the coronavirus, suppose the per-unit price of food increases by 25% (p1= $1.25), what is Katherine's new utility facing this price increase?

     (d) How much money would Katherine need to completely offset the harm from the price increase?

     (e) How much money would one have to take from Katherine to harm her as much as the price increase?

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Expert Solution

Rahul Sunny answered 6 months ago
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