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