EC201: Ted’s preferences over goods 1 (fuel) and 2 (food) are described by a utility function u(x1, x2) and satisfy non-satiation and convexity: Microeconomic Assignment, LSEP, Singapore

Question

Ted’s preferences over goods 1 (fuel) and 2 (food) are described by a utility function u(x1, x2) and satisfy non-satiation and convexity. For Ted, both fuel and food are normal goods.

• Define the compensating variation of a price increase.
• A fuel tax t is introduced raising the price of fuel from p1 to p1 + t. The price of food is unchanged. Illustrate the effect of the fuel tax on Ted’s budget constraint and on his uncompensated demand for fuel.
• To prevent protests over the rise in the price of fuel, the government gives Ted and others like him the compensating variation of the fuel price increase. Illustrate the effect of this on Ted’s demand for fuel. Can Ted’s fuel consumption be higher than when the price of fuel was p1?

Question

Pedro is an expected utility maximizer with a utility function u(W) = 2√
W, where W denotes wealth. Pedro’s initial wealth is 36, but he faces a risk of flood damage of 20 with a probability of 1/2 and no damage otherwise.

• Calculate Pedro’s expected utility and his expected wealth without insurance. Find his certainty equivalent and use it to explain why Pedro is risk-averse.
• Pedro can buy insurance at a premium p per unit. How much insurance will Pedro buy if premium p =1/2? Illustrate Pedro’s situation in a state-contingent income space diagram, clearly indicating Pedro’s wealth in the two states before and after purchasing insurance.
• Pedro’s situation can be viewed from two perspectives.

Perspective A: Wealth 36 and loses 20 with probability 1/2if it floods
Perspective B: Wealth 16 and gains 20 with probability 1/2 if it does not flood

Briefly explain why some decision-makers may view these two perspectives of the same situation differently.