Answer
b. The slope is -$\frac{1}{2}$. The opportunity cost of one candy bar is $\frac{1}{2}$ bags of peanuts. The opportunity cost of one bag of peanuts are two candy bars. The opportunity cost is constant.
c. No
d. The number of available combinations increases.
Work Step by Step
a. If I spend all my money for candy bars I can buy $\frac{15}{0 .75}$ = 20 candy bars and 0 peanut bags. Peanut bags are twice as expensive as candy bars; therefore I muss give up 2 candy bars for every bag of peanuts I buy. Our table starts at 20 candy bars and 0 peanuts and we decrease the number of candy bards by 2 for every one bag of peanuts. The expenditure is (number of candy bars) $\times$ \$0 .75 + (number of peanut bags) $\times$ \$1 .50; it is always equal to \$15 in our table, as we only look at the extreme, where we spend all our money.
b. At the two extremes we have 20 candy bars and 0 bags of peanuts or 10 bags of peanuts and 0 candy bars. Therefore, our graph connects the points (20, 0) and (0, 10). The slope of the line is the change in y divided by the change in x. If we give up one one bag of peanuts (or reduce y by 1) we gain 2 candy bars (or increase x by 2). The slope is, therefore, $\frac{-1}{2}$. Notice, this is equivalent to negative the price of candy divided by the price of peanuts.
c. The budget line tells us nothing about which available combination someone should or is going to chose. Everyone will evaluate his marginal costs and benefits and chose the option that increase his utility the most.
d. If we increase our budget the budget line gets shifted to the right. With a larger budget the number of available combinations increases. We can also see that the area under the budget line has increased.
