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August 22, 2014

Homework Help: graphs

Posted by Anonymous on Monday, February 5, 2007 at 11:36pm.

Students can buy a caffeine addict card for $50, which entitles them to a 25% discount on the price of coffee sold at the cafetaria. With coffee on horizontal axis and income on the vertical axis.
a)Draw budgent constraint of a studnet who buys such a card before and after the scheme is introduced.

is the budget constraints a linear line? What are the intercepts for both budget constraints?

Are you sure you want to put income on the y-axis?? If you do, then you would not have a budget constraint line. You would have a line, coming out of the origin, that shows the relationship between income and coffee consumption.

For a budget constraint line, the y-axis would have something like "all other goods" The budget constraint line is a downward sloping line that crosses the x and y axis on positive points. With e caffeine addict card, the budget constraint would shift a bit inward, but be flatter. That is, it would cross the y-axis at a lower point, but the x-axis at a higher point

I hope this helps. lotsa luck.

it says income on the vertical axis, but then it asks for the intercepts, so i am really confused.
How would the two graphs be different before and after the scheme?

I too am confused. You are asked to draw a "budget constraint" line and you are directed to put income on the y-axis. In my mind these are inconsistent with typical "budget constraint" type economic problems (which generally ask, given a level of income, how should a consumer spend that income among possible consumption choices.

Well, if you are sure you have the problem correctly recorded. Then:
In the initial case, make your graph with income on y axis, coffee in $ on the x axis. Draw a 45-degree line out of the origin. (y=x+0) This is a coffee budget constraint. It says, given any level of income, this is the most you could spend on coffee. For the coffee addict card, shift the budget constraint straight up by $50. The line becomes y=x+50. Here, first $50 of income go to buying the card, coffee consumption is zero. The slope of the line is still one (The x axis has dollars of coffee, so the relationship is still one-to-one.

(let me change something. Instead of "$ of coffee", put "number of cups of coffee" on the x axis and assume that a cup of coffee costs a dollar. The first line doesnt change; 100$ income gets a maximum of 100 cups, The new line with the card becomes y=.75x+50. That is, for each dollar of income above 50, the student could get 1.33 cups of coffee.


whew

Thanks, another question is...
On a seperate diagram, show the equilibrium of a student who is indifferent between buying the card or paying the standard price.
How would you draw this?

I would go back to what I think of as standard budget constraint analysis. Put coffee on the x axis, "everything else" on the y axis. Draw a downward sloping budget constraint line. Next, draw the alternative budget constraint line with the discount card. The new line should cross the y-axis at a lower point, but the x axis on a higher point. (i.e., the lines should cross). Now draw a single indifference curve that is tangent to both lines. QED

I hope this helps, lotsa luck

so the indifference curve should be tangent to the point they cross?

thanks a lot.

No.
The indifference curve should be above the point they cross. However, one side of the indifference curve should be tanget to the original constraint on a point to the left of the crossing point. The other side of the indifference curve should touch the new line at a point to the right.

(think of a ball in a corner. It can touch the wall and the floor at the same time, but doesnt touch the point where the wall and floor meet. )

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