Question

1. University shop sells beer and vodka. Mathematics students consume only beer and vodka A student has a stipend of W tenge that she can spend on her consumption. Find the budget set of the student in each of the following situations (you need to give analytical expressions for the budget line and draw it in beer-vodka space): (a) Price of a bottle of vodka is 5000 tenge and a bottle of beer is 1000 tenge. Stipend is 25000 tenge. (b) Price of a bottle of vodka is 3000 tenge and a bottle of beer is 1200 tenge. Stipend is 25000 tenge. (c) University decides that mixing beer with vodka harms students' grades. Therefore they order to introduce bundle pricing in the shop. Now there is a separate price for each bundle of goods vou buy. The price of a bundle consisting from x bottles of beer and y bottles of vodka is p(x, y1000x 2000y 100xy. Do you think this bundle pricing strategy may work to induce students not to mix beer with vodka? Explain your intuition. What are the opportunity cost of one bottle of vodka? Think if the opportunity costs are constant.

Answer 1

Let, x = quantity of bottles of beer

y = quantity of bottles of vodka

Given, that W = total stipend that can be spent on consumption

Now, a budget line is defined as $\inline \sum_{i=1}^{N} (Price * Quantity) = Total Budget (W)$

1) Budget line is: 1000x+5000y = 25000

where price of vodka bottle is 5000, quantity of vodka bottles is y

price of beer bottle is 1000, quantity of beer bottles is x

total budget is 25000

Thus, if the student buys 1 bottle of vodka for 5000, he/she can buy (25000 - 5000)/1000 ,i.e., 20 bottles of beer

Opportunity cost of one bottle of vodka is calculated as follows:

Opportunity cost of vodka is defined as: To buy one more bottle of vodka, the student will have to give up how many bottles of beer

Opportunity cost => (25000 - (5000*2))/1000 = 15

Thus, the student will have to give up 5 bottles of beer to buy one more bottle of vodka

Thus opportunity cost of one bottle of vodka is 5 bottles of beer

2) Similarly,

Budget line is: 1200x + 3000y = 25000

Opportunity cost => (25000 - (3000*2))/1200 = 15.833

Thus, the student will have to give up 3 bottles of beer to buy one more bottle of vodka

Thus opportunity cost of one bottle of vodka is 3 bottles of beer (to stay within stipend limit, the concept is you can't go beyond the budget constraint)

3) Price of bundle is: 1000x + 2000y + 100xy

In option 1 we needed 25000 tenge for 1 bottle of vodka and 20 bottles of beer

In option 3, we will need, Z tenge to buy 1 bottle of vodka and 20 bottles of beer

Z = 1000*20 + 2000*1 + 100*20*1

Z = 24,000 tenge which is lesser than 25000 tenge (the stipend of students)

In option 1,

When y = 0, x = 25

That is you can buy 25 bottles of beer for 25000 tenge

When x = 0, y = 5

That is you can buy 5 bottles of vodka for 25000 tenge

In option 3,

if we put y = 0, x = 25, total price is 25000

if we put x = 0, y = 5, total price is 10000

Thus, since bundle pricing doesn't really reduce the total cost of mixing up drinks, my intuition says that the bundle pricing strategy will not work to prevent students from mixing beer and vodka even though it makes buying only vodka cheaper.

Here, in 25000 tenge you can buy 25 bottles of beer and zero bottle of vodka

to buy one bottle of vodka, he has to give up around 5 bottles of beer ( he will have some surplus money after this) to remain within stipend of 25000

Opportunity cost of 1 bottle of vodka with bundle pricing strategy is 5 bottles of beer (considering only whole values)