Question

microeconomics

Bob goes to the supermarket to buy milk and cereal. He has $20 to spend. A consumption bundle consists of a quantity of milk, x (liters), and a quantity of cereal, y (grams). For all of the following questions you can assume that the consumption set is R2+. This means that milk and cereal can be consumed in any non-negative quantity.

1. (a) The price of milk at the supermarket is px = 4$/liter. The price of cereal is 0.2cents/gram. Draw Bob’s budget set. What is the slope of the budget line?

2. (b) Bob notices that the supermarket has a special coupon. A coupon states: “Buy 1 liter of milk and get 1 box of cereal for free”. A box of cereal has 2000 grams of cereal in it. Each shopper is limited to one coupon. Draw Bob’s budget set with 1 coupon. (Hint: Be careful with units again).

3. (c) Due to popular demand, the supermarket extends its special of- fer. Each customer is now allowed to use 2 coupons. Draw Bob’s budget set with 2 coupons.

4. (d) Finally, the supermarket decides to allow each customer to use an unlimited number of coupons. Draw Bob’s budget set if he has an unlimited number of coupons.

5. (e) Bob is smart and his friends are lazy. Bob’s friends know the prices at the supermarket but they do not know about the coupons. Bob offers to buy their cereal for them, and his friends agree to pay him exactly what they would have to pay for cereal at the supermarket, i.e., they will pay him 0.2cents/gram of cereal. Suppose that Bob’s friends are willing to buy an unlimited amount of cereal at this price. Bob’s budget set now consists of all consumption bundles he can afford given his wealth of $20, the prices at which he can buy milk and cereal at the supermarket, the unlimited number of coupons, and the price at which he can sell cereal to his friends. Draw the budget set.

Answer 1

a) The income of Bob is $

The price of milk (px) =$4/lit

The price of cerial (py)= 0.2 cents

The budget function of Bob will be

4x+ 0.2y =20

x= number of units of x (milk) bought

y = number of units of y (cereal) bought

The slope of the budget line is given by px/ py= 4/ 0.2 =20

b) The coupon gives 1 packet of cereal containing 2000 grams of cereal after buying 1 lit of milk.

The horizontal intercept would be 20/ 1= 20

The vertical intercept will be 20/0.2 = 100

The budget line of Bob for 1 coupon can be shown diagramatically as: