A consumer has a current income of k60, which can be spent only on goods X and Y. The price X is k3 and the price Y is k2.

Question

i. Graph the consumer's budget constraint, clearly labeling the intercepts and the slope of the budget line

Answer 1

To graph the consumer's budget constraint, we'll first need to find the intercepts and the slope of the budget line.

1. Intercepts:
To find the intercepts, we can set the budget constraint equation as follows:
3X + 2Y = 60

When X = 0:
3(0) + 2Y = 60
2Y = 60
Y = 30

So, the Y-intercept is 30.

When Y = 0:
3X + 2(0) = 60
3X = 60
X = 20

So, the X-intercept is 20.

2. Slope:
To find the slope, we can rearrange the budget constraint equation in terms of Y:
2Y = 60 - 3X
Y = 30 - (3/2)X

The coefficient of X (-3/2) is the slope of the budget line.

Now, we can plot the intercepts and draw the budget line on a graph with X on the horizontal axis and Y on the vertical axis. The slope of -3/2 means that for every unit increase in X, Y decreases by 1.5 units.

The budget line will pass through the points (0,30) and (20,0), with a slope of -3/2.