Question

In: Economics

Suppose that Andy has m to spend on poutine and salad. Suppose that poutine costs p...

Suppose that Andy has m to spend on poutine and salad. Suppose that poutine costs p dollars per ounce and salad costs q dollars per pound. The prime minister is worried that Quebec's national dish is contributing to an obesity problem. Therefore he has implemented a junk food tax. After the purchase of one large poutine (10 ounces), each additional ounce of poutine purchased is subjected to a tax of t dollars per ounce.

a) Draw Andy's budget constraint in the absence of the junk food tax on a graph with salad on the vertical axis and poutine on the horizontal axis. What is the maximum amount of salad that he can purchase? What is the maximum amount of poutine he can purchase?

b) What is the relative price of salad?

c) Draw Andy's budget set after the prime minister implements the junk food tax assuming that he has enough income to purchase more than one large poutine. What is the maximum amount of salad that he can purchase now? What is the maximum amount of poutine that he can purchase now?

d) What happens to the relative price of salad? Explain the intuition.

e) What happens to the budget set if Andy has enough money to purchase only 6 ounces of poutine?

f) Suppose that Andy has enough money to purchase 10 large poutines. Suppose that Andy considers poutine and salad to be perfect substitutes. What can you say about Andy's marginal rate of substitution of salad for poutine if he spends all his money on poutine before the implementation of the junk food tax and buys only one large poutine after the policy intervention?

Solutions

Expert Solution

Ans: There are two goods in the bundle: Salad and Poutine. Let X = Poutine, Y = Salad.

The cost of the good X is p, while the cost of the good Y is q. So, P1 = p, P2 = q.

Andy's Budget = m

Aftet purchase of one large Poutine(X) which is 10 ounce, each additional ounce will be taxed of t dollar per ounce. So, tax = t.

(a) Andy's Budget constraint in absence of tax is:

The graph of his budget constraint is:

  

Figure 1

We can see from the above figure that BB' is the budget line.

  • The maximum amount of Salad that Andy can purchase is at point B, which lies on the Y-axis. Suppose, maximum amount is n for Salad, then as per the assumption of Marginal rate of Substitution, Andy has to choose zero amount for Poutine.
  • The maximum amount of Poutine that Andy can purchase is at point B', which lies on the X-axis. Suppose, maximum amount is n for Poutine, then as per the assumption of Marginal rate of Substitution, Andy has to choose zero amount for Salad.

(b) A relative price of a good is comparable to the price of another good in a consumption bundle. Here, the price of good X = Poutine and Y = Salad is p and q respectively. Suppose, we indicate the relative price of Salad as (Pr)salad. The formula for the relative price of Y is price of good Y divided by the price of good X. Hence, the expression is as follows:

  

(c) Now, the Prime Minister will taxed assuming that he has enough money to purchase more than one large Poutine(X). The tax rate is = t. The figure is given below:

  

Figure 2

From the diagram above we can clearly see that after Andy has been taxed, his budget line shifted to its left from BB' to BB''. This implies that, after he has been taxed on the good X (Poutine), his quantity of consumption of Poutine decreased in order to satisfy his budget constraint. Since, a tax caused the price of Poutine (X) to increase.

  • Since there is no amount taxed on Salad, the maximum amount Andy can purchase remains the same which is at point B, which lies on the Y-axis. Suppose, maximum amount is n for Salad, then as per the assumption of Marginal rate of Substitution, Andy has to choose zero amount for Poutine.
  • Now that the tax on Poutine increased the price, the maximum amount of Poutine that Andy can purchase is at point B'', which lies on the X-axis. Suppose, maximum amount is n for Poutine, then as per the assumption of Marginal rate of Substitution, Andy has to choose zero amount for Salad.

(d) As we know that the relative price od Salad is:

  

Since, there is an increase in the price of Poutine, which is an increase in p. So, the denominator is larger than the numerator. This will futher decrease the the relative price of Salad.

(e) When Andy has enough money to buy 6 ounces of Poutine(X), there will be an increase in his budget (m). There will only be an increase in the quantity purchased by Andy which will further shift the budget line to its right from BB' forming a new budget line BB'''. Note that the purchase of Salad remains constan throughout.

The quantity of Poutine (X) purchased by Andy is 6ounces which is 1/16 th of a pound.The new budget line will be:

The diagram is given below.

Figure 3

(f) Considering Salad (Y) and Poutine (X) to be substitutes.

  • Before implementation of tax (t): Since X and Y are substitutes, Andy will go for spending all the money on Poutine (X), since there is no inclusion of tax. The Marginal rate of substitution is expressed as:

MUXis defined as the change in the utility with an additional unit of consumption of X.

MUYis defined as the change in the utility with an additional unit of consumption of Y.

Since, Andy will spend all of his money on X, the marginal utility of X will rise initially, reach at its peak of satiation and the finally decrease after consumption of an additional unit. The MRSXY will decrease due to a larger value of MUY compared to MUX.

  • After implementation of tax (t): X and Y are substitutes. Tax is been implemented on Poutine (X). Andy purchases only one large Poutine and spends rest of his income on Salad (Y). The Marginal rate of substitution is expressed as:

MUXis defined as the change in the utility with an additional unit of consumption of X.

MUYis defined as the change in the utility with an additional unit of consumption of Y.

Since, Andy will spend all of his money on Y, the marginal utility of Y will rise initially, reach at its peak of satiation and the finally decrease after consumption of an additional unit. The MRSXY will increase due to a larger value of MUX compared to MUY.


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