According to a CDC report, drinking too many sugary drinks (e.g., coke) can increase the likelihood of diabetes and other health issues. The local government thinks that coke's low price causes its high consumption. Hence, the government decides to charge a "sin tax" of $3 on coke, i.e., now the price of coke is $5, which is the same as the price of mineral water. Suppose Tianyu's budget is still $10. What are the "sin tax" policy's substitution effect, income effect, and the total effect on coke and soda consumption? Illustrate these three effects in a graph. Answer is below so draw the graph.

ANSWER WITHOUT THE GRAPH. DRAW GRAPH FOR THIS ANSWER:

Before the "sin tax," the price of coke is $2, and the price of mineral water is $5. The optimal consumption bundle is 2 cans of coke and 1 bottle of mineral water. The total expenditure is 2($2) + 1($5) = $9, which is within the budget constraint. After the "sin tax," the price of coke increases to $5, the same as mineral water. The budget constraint is still 2 + 5 = 10. Using the same method as before, the optimal consumption bundle is now 1 can of coke and 1 bottle of mineral water. The total expenditure is 1($5) + 1($5) = $10, which is exactly the budget constraint. The substitution effect is the change in consumption of coke due to the change in its relative price. In this case, the price of coke has increased by $3, which means the relative price of coke has increased. The substitution effect is the reduction in the consumption of coke due to this price increase, holding utility constant. Since coke and mineral water are not perfect substitutes, the substitution effect is negative, meaning that people will reduce their consumption of coke due to the price increase. The income effect is the change in consumption of coke due to the change in income, holding relative prices constant. In this case, the income effect is positive because the increase in the price of coke means that consumers have more income left to spend on other goods, including more mineral water. However, the income effect is small since the budget constraint has not changed.

The total effect is the sum of the substitution and income effects. In this case, the total effect is negative since the substitution effect dominates. This means that people will consume less coke after the "sin tax" policy.

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