1. John spends his income on pizza (1) and tacos (2). Pizza is priced at $2 and
ID: 1140864 • Letter: 1
Question
1. John spends his income on pizza (1) and tacos (2). Pizza is priced at $2 and tacos at $1 per unit. If John has an income of $50 to spend and his utility function is represented as U iven the utility function, the marginal utilities for pizza and tacos are MU 03 nd MU2-0.7 You can plot pizza on -axis and tacos on y-axis. 0.3,0.7 i. Find the marginal rate of substitution between goods 1 and 2. ii. Given the above information write down John's budget equation in terms of prices, quantities and income. iii. Find the slope of John's budget constraintExplanation / Answer
i. Marginal Rate of Substitution (MRS) is the rate at which John will give up some amount of Pizza for Tacos while maintaining the same level of satisfaction or utility. In this case, his Budget is constrained to his Income of $50.
Therefore, MRS equals - (Price of Pizza/Price of Taco) = - (2/1) =-2.
ii. Budget Equation :
Total Income = (Price of Pizza * Quantity of Pizza) + (Price of Taco * Quantity of Tacos)
50 = 2x1 + 1x2
iii. Slope of Budget Constraint = Price of Pizza/ Price of Taco
= 2/1 = 2
This indicates that Relative Price of 1 unit of Pizza is 2 units bof Taco.
iv. Optimal Consumption Bundle is the combination of Pizzas and Tacos that maximizes John's happiness or utility.
Therefore, MRS of Pizza and Tacos = Price of Pizza/ Price of Taco
Given that Budget Constraint is 50 = 2x1 + x2
Substituting, 25 in X 2 we get 50 = 2x1 + 25
50 - 25 = 2x1
x 1 = 25/2 = 12.5
v. Based on the calculation in answer iv., Optimal no. of Pizzas & Tacos that John will purchase equals his Optimal Consumption Bundle within his allotted Budget of $50.
12.5 units of Pizza & 25 units of Tacos form John's Optimal Consumption Bundle.
vi. The Original Utility Function was x 1 0.3 + x 2 0.7
The New Utility Function is 10x 1 0.3 + x 2 0.7 meaning Pizza is preferred 10 times to Taco.
The utility changes towards Pizza and John would consume highre Pizza than before to maximize his utility. This follows the cardinal school of utility theory, where utility can be measured in the unit 'utils'.
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