Question

1) Ben allocates his snack budget between two goods, chocolate and fruit. Write down his utility function and the equation of his budget line. What is the slope of his budget line, if chocolate is on the horizontal axis? If he uses all of his snack budget on chocolate, what is the maximum amount of chocolate he could purchase?

Answer 1

Answer

Ben allocates his snack budget between two goods, chocolate(C) and fruit(F).His utility(U) function is as follows.

U = U(C , F)

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Let, Ben's snack budget is 'M' , price of chocolate is 'Pc' and the price of fruit is 'Pf', then the equation of his budget line is as follows,

Pc * C + Pf * F = M

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If chocolate is measured on the horizontal axis, then fruit is measured on the vertical axis.

In general, the equation of a line can be written as,

Y = mX + b , where 'm' is the slope of the line, and 'b' is the vertical or Y-axis intercept.

Following the above equation of a line, we can write the equation of Ben's budget line as follows;

Pf * F = - Pc * C + M

Now, dividing both sides of the above equation by 'Pf', we get,

F = (- Pc / Pf) + (M / Pf)

In the above equation of the budget line, '- Pc / Pf' is the slope of the budget line , and 'M / Pf' is the vertical intercept, that shows the maximum amount of fruit, Ben can consume, if he doesn't consume chocolate.

The slope of the budget line = - Pc / Pf

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If Ben allocates all of his snack budget only in chocolate, he will purchase '0' amount of fruit.

So, Ben's equation of budget line will be,

Pc * C + 0 = M

Or,  Pc * C = M

Or, C = M / Pc

The maximum amount of chocolate, he could purchase is 'M / Pc' , i.e., 'Ben's budget / Price of chocolate'.

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