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Econ-UA 353-002 HW #1Due at the beginning of class on Wednesday September 28, late homework will NOT be accepted for any reason.Question 1. Consider an exchange economy with two goods, ale and bread.There are two individuals, Ann and Bob, whose initial endowments are as follows: Ann has 40 units of ale and 20 units of bread, and Bob has 20 units ofale and 40 units of bread. The utility from consuming a1 ale and b1 bread is13u1 (a1 , b1 ) = (a1 ) 4 (b1 ) 4 for Ann, and the utility from consuming a2 ale and b211bread is u2 (a2 , b2 ) = (a2 ) 2 (b2 ) 2 for Bob.(1) If we normalize the price of bread to 1, for an arbitrary ale price p (relativeto bread), given Annâs endowments, what is the demand for ale and bread forAnn?(2) If we normalize the price of bread to 1, for an arbitrary ale price p (relativeto bread), given Bobâs endowments, what is the demand for ale and bread forBob?(3) What is the price that will clear both markets?(4) What is the competitive equilibrium allocation for this exchange economy?Is it Pareto efficient?Question 2. (Leach textbook, Ch.2 Q1)Consider an exchange economy with two goods, ale and bread, and two individuals, George and Harriet. For each of the situations below, draw an Edgeworthbox containing an endowment point and a budget line. Use ale as the horizontalaxis, bread the vertical axis, put Georgeâs origin point in the bottom-left cornerof the box and Harrietâs origin point in the top-right corner of the box.(1) Draw an indifference curve for George and an indifference curve for Harriet,both tangent to the budget line, such that George wants to buy ale, Harrietwants to sell ale, and George wants to buy more ale than Harriet wants to sell.(2) Draw two indifference curves, both tangent to the budget line, such thatGeorge and Harriet both want to buy ale.(3) Draw two indifference curves, both tangent to the budget line, such that thecurrent price is market-clearing but no goods are traded.1Question 3. (Gruber textbook, Ch.5 Q16)One hundred commuters need to use a strip of highway to get to work. They alldrive alone and prefer to drive big cars – it gives them more prestige and makesthem feel safer. Bigger cars cost more per mile to operate, however, since theirgas mileage is lower. Worse yet, bigger cars cause greater permanent damageto roads.The weight of the car is w. Suppose that the benefits from driving are 12w,while the costs are 3w2 . The damage to roads is 2w3 . Assume that individualshave utility functions of the form U = x, where x are the net benefits fromdriving a car of a given size.(1) What car weight will be chosen by drivers?(2) What is the optimal car weight? If this differs from (1), why does it?(3) Can you design a toll system that causes drivers to choose the optimal carweight? If so, then how would such a system work (e.g., how might the tolldepend on the car)?Question 4. Suppose that a honey farm is located next to an apple orchard.Let the amount of apples produced be denoted by a and the amount of honeyproduced be denoted by h. The cost functions of the two firms are cH (h) =and cA (a) =a2100? h. The price of honey is $2 and the price of apples is$3. (i.e. The profit functions of the two firms are ?H (h) = 2h ??A (a) = 3a ?a2( 100h2100h2100and? h). )(1) If the firms each operate independently, what would be the amount of honeyand apples produced?(2) Suppose that the honey and apple firms merge to one big firm. What wouldbe the profit-maximizing output of honey and apples for the combined firm?(3) If the firms stay separate, and the government provides the honey producerwith a subsidy of $s per unit of honey produced. How much would s be toinduce the same honey output as in (2)?
