ECO 210: INTERMEDIATE MICROECOMICSCAT 1 1. A consumer’s preference are represented by the following utility function0.5 U ( x , y )=x + ya) Obtain the MRS x , yx , y >0 of the consumer at an arbitrary point ( x , y ¿ where (4mks) b) Suppose the price of the second good (y) is 1, and the price of the first good (x) isdenoted by p> 0. If the consumer’s income is m> 0, obtain the optimal consumptionbundle of the consumer (in terms of m and p). (7mks)2. Joe considers beer and soda to be perfect substitutes at a rate of 1:2, that is, he alwaysreceives the same utility if he has one beer or two sodas to drink. He spends $12 a day ondrinks, and beers cost $3 while sodas cost $1 each. However, one day the price of beersdecreases to $2; there is no change in his budget.a) How does consumption change when the price of beers changes? What is Joe’s newlevel of utility? (3 mks)b) Show with the aid of a graph what happens to the optimal allocation and the level ofutility when the price of beer changes. (3mksc) How much must Joe’s budget decrease to return him to the original utility level?(3 mks)

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