(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 109

84 PART • Producers, Consumers, and Competitive Markets Using equation (3.1), we can see how much of C must be given up to consume more of F We divide both sides of the equation by PC and then solve for C: C = (I/PC) - (PF/PC)F (3.2) Equation (3.2) is the equation for a straight line; it has a vertical intercept of I/PC and a slope of −(PF/PC ) The slope of the budget line, −(PF/PC ), is the negative of the ratio of the prices of the two goods The magnitude of the slope tells us the rate at which the two goods can be substituted for each other without changing the total amount of money spent The vertical intercept (I/PC ) represents the maximum amount of C that can be purchased with income I Finally, the horizontal intercept (I/PF ) tells us how many units of F can be purchased if all income were spent on F The Effects of Changes in Income and Prices We have seen that the budget line depends both on income and on the prices of the goods, PF and PC But of course prices and income often change Let’s see how such changes affect the budget line INCOME CHANGES What happens to the budget line when income changes? From the equation for the straight line (3.2), we can see that a change in income alters the vertical intercept of the budget line but does not change the slope (because the price of neither good changed) Figure 3.11 shows that if income is doubled (from $80 to $160), the budget line shifts outward, from budget line L1 to budget line L2 Note, however, that L2 remains parallel to L1 If she desires, our consumer can now double her purchases of both food and clothing Likewise, if her income is cut in half (from $80 to $40), the budget line shifts inward, from L1 to L3 Clothing (units per week) 80 F IGURE 3.11 60 EFFECTS OF A CHANGE IN INCOME ON THE BUDGET LINE A change in income (with prices unchanged) causes the budget line to shift parallel to the original line (L1) When the income of $80 (on L1) is increased to $160, the budget line shifts outward to L2 If the income falls to $40, the line shifts inward to L3 40 20 L1 L3 L2 (I = $40) (I = $80) 40 80 (I = $160) 120 Food 160 (units per week)